When do matrices B and C commute?
alainv...@gmail.com
matrices.
Ex1: if B = A^ n , C = A^ p , n, p integer numbers
B*C = C*B = A ^ (n+p)
Ex2: more generally B = p1(A) ,C = p2(A) p1 and p2 polynomials
then B*C = C*B = p3(A) ; p3(u) = p2(u)*p1(u) = p1(u)*p2(u) ,
I've built a case B = {[18,27,36],[48,66,84],[28,40,52]}
C = {[5,10,15], [20,25,30] ,[10,15,20]}
There is probably an extension to some kinds of function f1,f2
B = f1(A) , C = f2(A)
Your comments will be welcomed,
Alain
Arturo Magidin
alainv...@gmail.com <alainv...@gmail.com> wrote:
>I think about a needed parenthood between both the
>matrices.
>Ex1: if B = A^ n , C = A^ p , n, p integer numbers
> B*C = C*B = A ^ (n+p)
But that is not the only time it happens.
>Ex2: more generally B = p1(A) ,C = p2(A) p1 and p2 polynomials
>then B*C = C*B = p3(A) ; p3(u) = p2(u)*p1(u) = p1(u)*p2(u) ,
>I've built a case B = {[18,27,36],[48,66,84],[28,40,52]}
> C = {[5,10,15], [20,25,30] ,[10,15,20]}
These conditions are sufficient, but they are not necessary.
For example, take B = [0,0;0,1] and C = [1,0;0,0]. Then
BC=CB=[0,0;0,0] (where [a,b;c,d] is the 2 x 2 matrix with first row
[a,b] and second row [c,d]), but B and C are not polynomial
expressions on the same matrix.
More generally, if B and C, considered as linear transformations, have
im(B) contained in null(C) and im(C) contained null(B), then their
product in either order will be equal to the zero matrix; but if the
images of B and C have trivial interesection without either being
trivial, in general you will not have that they are polynomial
expressions of the same matrix. You can have nonzero products as
well, so long as B behaves 'well enough' on the image of C and
vice-versa.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================
Arturo Magidin
magidin-at-member-ams-org
amy666
i believe matrix A and B commute if
- assuming they have abs different from 1 or 0 -
- assuming both are square matrices -
if A^C = B for some square matrix C
where C satisfies C D = D C for any square matrix D.
- assuming all matrices are of the same size of course -
hope that answers your question
( this is consistant with the polysigned - if anyone cares - and also with all tetration conjectures )
high regards
tommy1729
Mariano Suárez-Alvarez
> alain wrote :
>
>
>
> > I think about a needed parenthood between both the
> > matrices.
> > Ex1: if B = A^ n , C = A^ p , n, p integer
> > numbers
> > B*C = C*B = A ^ (n+p)
>
> > Ex2: more generally B = p1(A) ,C = p2(A) p1 and
> > p2 polynomials
> > then B*C = C*B = p3(A) ; p3(u) = p2(u)*p1(u) =
> > p1(u)*p2(u) ,
> > I've built a case B =
> > {[18,27,36],[48,66,84],[28,40,52]}
> > C = {[5,10,15], [20,25,30]
> > = {[5,10,15], [20,25,30] ,[10,15,20]}
>
> > There is probably an extension to some kinds of
> > function f1,f2
> > B = f1(A) , C = f2(A)
>
> > Your comments will be welcomed,
>
> > Alain
>
> i believe matrix A and B commute if
>
> - assuming they have abs different from 1 or 0 -
What is "abs"?
> - assuming both are square matrices -
There is no possible way two non-square matrices
can commute, for in that case the two products
have different sizes...
> if A^C = B for some square matrix C
>
> where C satisfies C D = D C for any square matrix D.
The only matrices C which commute with all other matrices
are the scalar matrices, that is, the scalar multiples
of the identity. In that case, and assuming that
by A^C you mean the conjugation of A by C, one
trivially has A^C = A.
> - assuming all matrices are of the same size of course -
If they are not, the question does not make sense.
-- m
amy666
abs = absolute value = determinant
>
> > - assuming both are square matrices -
>
> There is no possible way two non-square matrices
> can commute, for in that case the two products
> have different sizes...
thats why i assumed it of course :)
>
> > if A^C = B for some square matrix C
> >
> > where C satisfies C D = D C for any square matrix
> D.
>
> The only matrices C which commute with all other
> matrices
> are the scalar matrices, that is, the scalar
> multiples
> of the identity.
the OP asked specificly for two matrices commuting with eachother.
In that case, and assuming that
> by A^C you mean the conjugation of A by C, one
> trivially has A^C = A.
no with ^ i mean power !!!
>
> > - assuming all matrices are of the same size of
> course -
>
> If they are not, the question does not make sense.
again thats why i assumed and wrote that.
>
> -- m
all clear now ?
regards
tommy1729
Gerry Myerson
<07d01995-8eed-4d69...@k36g2000pri.googlegroups.com>,
"alainv...@gmail.com" <alainv...@gmail.com> wrote:
Commuting matrices are simultaneously diagonalizable,
so in particular they have the same eigenvectors. I think
having the same eigenvectors and the same Jordan block
structure may be necessary and sufficient for commuting.
Anyway, I've given you some keywords to look for.
--
Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)
Mariano Suárez-Alvarez
wrote:
> In article
> <07d01995-8eed-4d69-bb87-df362b699...@k36g2000pri.googlegroups.com>,
>
> "alainvergh...@gmail.com" <alainvergh...@gmail.com> wrote:
> > I think about a needed parenthood between both the
> > matrices.
> > Ex1: if B = A^ n , C = A^ p , n, p integer numbers
> > B*C = C*B = A ^ (n+p)
>
> > Ex2: more generally B = p1(A) ,C = p2(A) p1 and p2 polynomials
> > then B*C = C*B = p3(A) ; p3(u) = p2(u)*p1(u) = p1(u)*p2(u) ,
> > I've built a case B = {[18,27,36],[48,66,84],[28,40,52]}
> > C = {[5,10,15], [20,25,30] ,[10,15,20]}
>
> > There is probably an extension to some kinds of function f1,f2
> > B = f1(A) , C = f2(A)
>
> > Your comments will be welcomed,
>
> Commuting matrices are simultaneously diagonalizable,
> so in particular they have the same eigenvectors. I think
> having the same eigenvectors and the same Jordan block
> structure may be necessary and sufficient for commuting.
> Anyway, I've given you some keywords to look for.
The matrices
0 0 0 0 0 0
1 0 0 1 0 0
0 1 0 0 2 0
are both nilpotent of index 3. The share
eigenvectors and subspaces of generalized
eigenvectors, yet they do not commute.
-- m
Gerry Myerson
<c6e54cf5-9f93-42e0...@n10g2000yqm.googlegroups.com>,
Mariano Suárez-Alvarez <mariano.su...@gmail.com> wrote:
You may be right, but humor me a little, because
I'm rusty on my generalized eigenvectors:
Each matrix has v = (0, 0, 1) as an eigenvector.
A generalized eigenvector w satisfies A w = v.
For the first matrix, we can take w = (0, 1, 0);
for the second, (0, 1/2, 0); but there is no w that works
for both matrices. So there is no matrix P such that
P^{-1} A P is in Jordan form for both matrices; they
are not "simultaneously Jordanalizable," if there is
such a term. I think that's what you need for
the matrices to commute.
Mariano Suárez-Alvarez
wrote:
> In article
> <c6e54cf5-9f93-42e0-b799-06770220f...@n10g2000yqm.googlegroups.com>,
There is a difference between "having the same Jordan
block structure and the same eigenvectors", which was
what you mentioned in the post I was replying to, and
"being simultaneously Jordanizable", which is what you
are saying in your last post. My example was intended
to make the difference more evident.
-- m
Gerry Myerson
<b9f62547-4b17-448c...@v13g2000yqm.googlegroups.com>,
Mariano Suárez-Alvarez <mariano.su...@gmail.com> wrote:
Good, point taken. I think my point was that although your matrices
have the same spaces of generalized eigenvectors, they don't have
the same generalized eigenvectors. I'm still not sure what the right
answer is (to the question about conditions under which matrices
commute).
Denis Feldmann
> alain wrote :
>
>> I think about a needed parenthood between both the
>> matrices.
>> Ex1: if B = A^ n , C = A^ p , n, p integer
>> numbers
>> B*C = C*B = A ^ (n+p)
>>
>> Ex2: more generally B = p1(A) ,C = p2(A) p1 and
>> p2 polynomials
>> then B*C = C*B = p3(A) ; p3(u) = p2(u)*p1(u) =
>> p1(u)*p2(u) ,
>> I've built a case B =
>> {[18,27,36],[48,66,84],[28,40,52]}
>> C = {[5,10,15], [20,25,30]
>> = {[5,10,15], [20,25,30] ,[10,15,20]}
>>
>> There is probably an extension to some kinds of
>> function f1,f2
>> B = f1(A) , C = f2(A)
>>
>> Your comments will be welcomed,
>>
>> Alain
>
> i believe matrix A and B commute if
As usual, your beliefs mean nothing
>
> - assuming they have abs different from 1 or 0 -
What is abs?
>
> - assuming both are square matrices -
>
> if A^C = B for some square matrix C
What is A^C ?
>
> where C satisfies C D = D C for any square matrix D.
>
You dont even know that such a C is necessarily of the form kI (i.e. the
diagonal matrix of value k on the diagonal, 0 elsewhere). So what do
you know?
> - assuming all matrices are of the same size of course -
>
>
> hope that answers your question
>
> ( this is consistant with the polysigned - if anyone cares - and also with all tetration conjectures )
>
Yes, as it is consistent with your usual style...
>
> high regards
>
> tommy1729
Denis Feldmann
alainv...@gmail.com
>
> - Afficher le texte des messages précédents -
Bonjour,
The both given nilpotent matrices might be considered
as cubic 'roots' of the null matrix.
If we want to work with integer powers (all Z ) we must
discard non inversible ones ,that is : singular matrices.
However a null matrix may be equals to pCA) , p a non
null polynomial (p might be the minimal or the characteristic
poly of A) .
Can we write A^0 = Id Identity matrix ?
coherent with A*Id = Id*A or A^1 * A^0 = A^0 *A^1 = A^(0+1)=A
In which cases C^(1/p) p-> inf. = C^0 = Id
Amicalement,
Alain
victor_me...@yahoo.co.uk
> For example, take B = [0,0;0,1] and C = [1,0;0,0]. Then
> BC=CB=[0,0;0,0] (where [a,b;c,d] is the 2 x 2 matrix with first row
> [a,b] and second row [c,d]), but B and C are not polynomial
> expressions on the same matrix.
Oh yeas they are! C = I - B, that is C = f(B) where f(x)= 1 - x.
Victor Meldrew
"I don't believe it!"
David C. Ullrich
wrote:
>alain wrote :
>
>> I think about a needed parenthood between both the
>> matrices.
>> Ex1: if B = A^ n , C = A^ p , n, p integer
>> numbers
>> B*C = C*B = A ^ (n+p)
>>
>> Ex2: more generally B = p1(A) ,C = p2(A) p1 and
>> p2 polynomials
>> then B*C = C*B = p3(A) ; p3(u) = p2(u)*p1(u) =
>> p1(u)*p2(u) ,
>> I've built a case B =
>> {[18,27,36],[48,66,84],[28,40,52]}
>> C = {[5,10,15], [20,25,30]
>> = {[5,10,15], [20,25,30] ,[10,15,20]}
>>
>> There is probably an extension to some kinds of
>> function f1,f2
>> B = f1(A) , C = f2(A)
>>
>> Your comments will be welcomed,
>>
>> Alain
>
>i believe matrix A and B commute if
>
>- assuming they have abs different from 1 or 0 -
>
>- assuming both are square matrices -
>
>if A^C = B for some square matrix C
What in the world might you mean by A^C in this case?
>where C satisfies C D = D C for any square matrix D.
>
>- assuming all matrices are of the same size of course -
>
>
>hope that answers your question
>
>( this is consistant with the polysigned - if anyone cares - and also with all tetration conjectures )
>
>
>high regards
>
>tommy1729
David C. Ullrich
"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
Arturo Magidin
Fair enough. Make them 3 x 3 so there is a 0 in between in the
diagonal; or change the 1 in B to a 3 and the 1 in C to 2.
Arturo Magidin
Gerry Myerson <ge...@maths.mq.edi.ai.i2u4email> wrote:
>> There is a difference between "having the same Jordan
>> block structure and the same eigenvectors", which was
>> what you mentioned in the post I was replying to, and
>> "being simultaneously Jordanizable", which is what you
>> are saying in your last post. My example was intended
>> to make the difference more evident.
>
>Good, point taken. I think my point was that although your matrices
>have the same spaces of generalized eigenvectors, they don't have
>the same generalized eigenvectors.
Ehr... that doesn't make any sense. The space of generalized
eigenvectors consists of all generalized eigenvectors and the zero
vector. If their spaces of generalized eigenvectors are the same, then
they ->do<- have the same generalized eigenvectors, by definition.
You ->might<- mean that their cycles of generalized eigenvectors are
not equal (or not of equal length)...
victor_me...@yahoo.co.uk
> In article <53fc26e0-6567-4269-b02d-23935ea39...@g38g2000yqn.googlegroups.com>,
>
> <victor_meldrew_...@yahoo.co.uk> wrote:
> >On 19 Nov, 19:24, magi...@math.berkeley.edu (Arturo Magidin) wrote:
>
> >> For example, take B = [0,0;0,1] and C = [1,0;0,0]. Then
> >> BC=CB=[0,0;0,0] (where [a,b;c,d] is the 2 x 2 matrix with first row
> >> [a,b] and second row [c,d]), but B and C are not polynomial
> >> expressions on the same matrix.
>
> >Oh yeas they are! C = I - B, that is C = f(B) where f(x)= 1 - x.
>
> Fair enough. Make them 3 x 3 so there is a 0 in between in the
> diagonal; or change the 1 in B to a 3 and the 1 in C to 2.
And in each of these examples there will be a matrix A and polynomials
f and g with B = f(A) and C = g(A). (At least if we are working over
an infinite field ...). Over an infinite field, one won't get a
counterexample with diagonal matrices (think Lagrange interpolation).
Arturo Magidin
<victor_me...@yahoo.co.uk> wrote:
>And in each of these examples there will be a matrix A and polynomials
>f and g with B = f(A) and C = g(A). (At least if we are working over
>an infinite field ...). Over an infinite field, one won't get a
>counterexample with diagonal matrices (think Lagrange interpolation).
Good point. I'm sure some simple example with 2 x 2 or 3 x 3 will
exist...
victor_me...@yahoo.co.uk
> In article <523d6959-452e-4082-bb78-f5b08986a...@t11g2000yqg.googlegroups.com>,
>
> <victor_meldrew_...@yahoo.co.uk> wrote:
> >And in each of these examples there will be a matrix A and polynomials
> >f and g with B = f(A) and C = g(A). (At least if we are working over
> >an infinite field ...). Over an infinite field, one won't get a
> >counterexample with diagonal matrices (think Lagrange interpolation).
>
> Good point. I'm sure some simple example with 2 x 2 or 3 x 3 will
> exist...
Not for 2 x 2. I suspect that the unit matrices E_12 and E_13 work
for 3 x 3.
David C. Ullrich
Denis Feldmann <denis.feldm...@neuf.fr> wrote:
That's what I assumed. So tell me: What in the world
do you think that A^C is, if A and C are 2x2 matrices.
What _is_ "A to the power C"?
> >
> >>> - assuming all matrices are of the same size of
> >> course -
> >>
> >> If they are not, the question does not make sense.
> >
> > again thats why i assumed and wrote that.
> >
> >
> >> -- m
> >
> > all clear now ?
> >
> > regards
> >
> > tommy1729
--
David C. Ullrich
Robert Israel
Yes. The only 3x3 matrices that commute with both E_12 and E_13 are of
the form A = a I + b E_12 + c E_13, and then
f(A) = f(a) I + f'(a) b E_12 + f'(a) c E_13.
--
Robert Israel isr...@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
galathaea
> So tell me: What in the world
> do you think that A^C is, if A and C are 2x2 matrices.
>
> What _is_ "A to the power C"?
wouldn't that just be
exp(C ln(A))?
both exp and ln
may be defined on square matrices
using the power series
(though there may be convergence to consider)
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
amy666
> In article
> <b9f62547-4b17-448c...@v13g2000yqm.goog
> legroups.com>,
> Mariano Suárez-Alvarez
..
I'm still not sure
> what the right
> answer is (to the question about conditions under
> which matrices
> commute).
perhaps the answer given by tommy1729 ...
>
> --
> Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for
> email)
regards
tommy1729
amy666
> On Nov 20, 10:58 am, "David C. Ullrich"
> <dullr...@sprynet.com> wrote:
>
> > So tell me: What in the world
> > do you think that A^C is, if A and C are 2x2
> matrices.
> >
> > What _is_ "A to the power C"?
>
> wouldn't that just be
>
> exp(C ln(A))?
yep thats it.
and before objections are made , i said det =/= [0;1]
>
> both exp and ln
> may be defined on square matrices
> using the power series
> (though there may be convergence to consider)
perhaps i should try to sell a book too , like david.
yeah , ill sell david ullrich a book about subjects like :
continu iterations ( gamma , Barnes G , tetration , moebius transforms etc )
matrix powers ( A^C )
polysigned ( with credit to timothy )
large cardinal axioms ( it was strange nobody noticed these missing in the ' disproofs ' of TST and aleph_aleph_0 is max , they assumed the large cardinals could be proven to exist just with ZF ... )
>
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
> galathaea: prankster, fablist, magician, liar
regards
tommy1729
Gerry Myerson
mag...@math.berkeley.edu (Arturo Magidin) wrote:
> In article <gerry-23929A....@sunb.ocs.mq.edu.au>,
> Gerry Myerson <ge...@maths.mq.edi.ai.i2u4email> wrote:
> >> There is a difference between "having the same Jordan
> >> block structure and the same eigenvectors", which was
> >> what you mentioned in the post I was replying to, and
> >> "being simultaneously Jordanizable", which is what you
> >> are saying in your last post. My example was intended
> >> to make the difference more evident.
> >
> >Good, point taken. I think my point was that although your matrices
> >have the same spaces of generalized eigenvectors, they don't have
> >the same generalized eigenvectors.
>
> Ehr... that doesn't make any sense. The space of generalized
> eigenvectors consists of all generalized eigenvectors and the zero
> vector. If their spaces of generalized eigenvectors are the same, then
> they ->do<- have the same generalized eigenvectors, by definition.
>
> You ->might<- mean that their cycles of generalized eigenvectors are
> not equal (or not of equal length)...
Earlier in the thread there was a lot of stuff which included my hazy
recollection of the definition of generalized eigenvector and an
example that illustrated it.
So I'll repeat it.
The matrices A and B given by
0 0 0
1 0 0
0 1 0
and
0 0 0
1 0 0
0 2 0
both have eigenvalue 0. Taking v = (0, 0, 1) as a common eigenvector,
a solution of A x = v is the generalized eigenvector (0, 1, 0), but
a solution of B x = v is the generalized eigenvector (0, 1/2, 0).
The generalized eigenspaces are the same, but there is no single
vector x that satisfies both A x = v and B x = v. Perhaps what I am
pointing out is something about what you call "cycles of generalized
eigenvectors."
Gerry Myerson
> In article <gerry-23929A....@sunb.ocs.mq.edu.au>,
> Gerry Myerson <ge...@maths.mq.edi.ai.i2u4email> wrote:
> >> There is a difference between "having the same Jordan
> >> block structure and the same eigenvectors", which was
> >> what you mentioned in the post I was replying to, and
> >> "being simultaneously Jordanizable", which is what you
> >> are saying in your last post. My example was intended
> >> to make the difference more evident.
> >
> >Good, point taken. I think my point was that although your matrices
> >have the same spaces of generalized eigenvectors, they don't have
> >the same generalized eigenvectors.
>
> Ehr... that doesn't make any sense. The space of generalized
> eigenvectors consists of all generalized eigenvectors and the zero
> vector. If their spaces of generalized eigenvectors are the same, then
> they ->do<- have the same generalized eigenvectors, by definition.
>
> You ->might<- mean that their cycles of generalized eigenvectors are
> not equal (or not of equal length)...
In any event, my suggestion that commuting is the same as simultaneous
Jordaning is incorrect. The matrices A and B given by
1 1 0
0 1 0
0 0 2
and
3 0 0
0 4 1
0 0 4
are both in Jordan form (so a fortiori they are simultaneously
Jordanable), they even have the same Jordan block structure,
but they do not commute. I give up. I don't know what theorem,
if any, characterizes commuting matrices in terms of simultaneous
somethingizability.
Mariano Suárez-Alvarez
wrote:
> In article <gg3tec$2mf...@agate.berkeley.edu>,
> magi...@math.berkeley.edu (Arturo Magidin) wrote:
>
>
>
> > In article <gerry-23929A.17225620112...@sunb.ocs.mq.edu.au>,
Well, if you go further, you are going to arrive evidently
at the condition
A and B are simultaneosly jordanizable,
with the same block structure.
This condition immediately implies that they commute.
Is is necessary for commutation?
-- m
Robert Israel
... depending on what you mean by "the same Jordan block structure".
But you should also note that
[ 0 1 0 ] [ 0 0 1 ]
[ 0 0 1 ] [ 0 0 0 ]
[ 0 0 0 ] and its square [ 0 0 0 ]
do _not_ have the same Jordan block structure, and can't be simultaneously
Jordanized, but do commute.
> but they do not commute. I give up. I don't know what theorem,
> if any, characterizes commuting matrices in terms of simultaneous
> somethingizability.
--
Mariano Suárez-Alvarez
wrote:
> In article <gg3tec$2mf...@agate.berkeley.edu>,
> magi...@math.berkeley.edu (Arturo Magidin) wrote:
>
>
>
> > In article <gerry-23929A.17225620112...@sunb.ocs.mq.edu.au>,
Notice that two matrices which commute have the
same invariant subspaces. In your example, this condition
does not hold (consider the subspace spanned by
(0,1,0) and (0,0,1)). This implies that not only
the sizes and multiplicities of the Jordan blocks are
the same, but that the corresponding direct sum
decomposition of the space are the same. This is what's
failing in your example.
-- m
Robert Israel
where k_i = 1 + sum_{j < i} n_j) corresponding to eigenvalues lambda_i,
i=1..k. Then the requirement on B is that each (i,j) block
(i.e. for rows k_i to k_i+n_i-1 and columns k_j to k_j+n_j-1)
is all 0 if lambda_i <> lambda_j, while if lambda_i = lambda_j
it is upper triangular (i.e. B_{k_i + r, k_j + s} = 0 if
s < r + max(0,n_j-n_i)) and Toeplitz (i.e. B_{k_i+r+1,k_j+s+1} =
B_{k_i+r,k_j+s} for 0 <= r <= n_i - 2, 0 <= s <= n_j - 2).
For example, the matrices that commute with
[ 0 1 0 0 0 ]
[ 0 0 0 0 0 ]
[ 0 0 0 1 0 ]
[ 0 0 0 0 1 ]
[ 0 0 0 0 0 ] (n_1 = 2, n_2 = 3, lambda_1 = lambda_2 = 0)
are all those of the form
[m[1, 1] m[1, 2] 0 m[1, 4] m[1, 5]]
[ ]
[ 0 m[1, 1] 0 0 m[1, 4]]
[ ]
[m[3, 1] m[3, 2] m[3, 3] m[3, 4] m[3, 5]]
[ ]
[ 0 m[3, 1] 0 m[3, 3] m[3, 4]]
[ ]
[ 0 0 0 0 m[3, 3]]
while those that commute with
[ a 1 0 0 0 ]
[ 0 a 0 0 0 ]
[ 0 0 b 1 0 ]
[ 0 0 0 b 1 ]
[ 0 0 0 0 b ]
with a <> b are those of the form
[m[1, 1] m[1, 2] 0 0 0 ]
[ ]
[ 0 m[1, 1] 0 0 0 ]
[ ]
[ 0 0 m[3, 3] m[3, 4] m[3, 5]]
[ ]
[ 0 0 0 m[3, 3] m[3, 4]]
[ ]
[ 0 0 0 0 m[3, 3]]
Robert Israel
Somehow the first line of my posting got lost. It should have been:
OK, let's try this. Suppose A is in Jordan form, with diagonal blocks of
Arturo Magidin
Gerry Myerson <ge...@maths.mq.edi.ai.i2u4email> wrote:
>In article <gg3tec$2mf2$1...@agate.berkeley.edu>,
> mag...@math.berkeley.edu (Arturo Magidin) wrote:
[...]
Yup. The corresponding cycles are different.
As it happens, I just finished teaching the Jordan Canonical Form (out
of Friedberg, Insell and Spence). So here goes:
If k is an eigenvalue of A, then the eigenvectors of A associated to k
are the nonzero vectors such that Av = kv. Equivalently, the nonzero
vectors in the nullspace of A-kI.
The eigenspace associated to k is the nullspace of A-kI, often
denoted E_k.
A generalized eigenvector associated to k is a nonzero vector v such
that there exists some p>0 with (A-kI)^p(v) = 0. The generalized
eigenspace associated to k is the collection of all vectors in the
union of the nullspaces of the (A-kI)^p; it is not hard to check that
it is enough to take nullspace(A-kI)^m, where m is the algebraic
multiplicity of k as an eigenvalue of A.
A Jordan canonical basis is constructed by making a basis which is a
disjoint union of "cycles of generalized eigenvectors", each such
cycle yielding one of the blocks. If v is a generalized eigenvector
associated to k, and p is the smallest positive integer such that
(A-kI)^p(v)=0, then the cycle of generalized eigenvectors generated by
v is the (ordered) set of vectors
(A-kI)^{p-1)(v), (A-kI)^{p-2}(v), ..., (A-kI)(v), v.
In this cycle, the vector (A-kI)^{p-1}(v) is the only eigenvector,
though they are all generalized eigenvectors. This is called the
"initial vector" of the cycle.
Your observation is that in the matrices above, the cycles of
generalized eigenvectors are distinct, so that you cannot have a the
same cycle in a basis that will function for both matrices as a Jordan
canonical basis. However, both the eigenspaces and the generalized
eigenspaces of the two matrices are equal; it's the action of the
matrix on the generalized eigenspace (the "cyclic structure", as it
were) that differs.
Gerry Myerson
<28ee96ee-9f4a-4d3c...@u14g2000yqg.googlegroups.com>,
Mariano Suárez-Alvarez <mariano.su...@gmail.com> wrote:
> Well, if you go further, you are going to arrive evidently
> at the condition
>
> A and B are simultaneosly jordanizable,
> with the same block structure.
>
> This condition immediately implies that they commute.
> Is is necessary for commutation?
No, and I'm sorry I ever wrote anything to suggest it.
If, for example, A is
1 1
0 1
and B = 2 A, then of course A and B commute,
but P^{-1} B P = 2 P^{-1} A P can't be in Jordan form
if P^{-1} A P is.
Gerry Myerson
but haven't taught JCF in a while, so most of it went away.
David C. Ullrich
wrote:
>galathaea wrote :
>
>> On Nov 20, 10:58 am, "David C. Ullrich"
>> <dullr...@sprynet.com> wrote:
>>
>> > So tell me: What in the world
>> > do you think that A^C is, if A and C are 2x2
>> matrices.
>> >
>> > What _is_ "A to the power C"?
>>
>> wouldn't that just be
>>
>> exp(C ln(A))?
>
>yep thats it.
That's funny - you need someone else to say what you meant.
Why is it that and not, say, exp(ln(A) C)?
And exactly what do you mean by ln(A)? I didn't
bother asking galathea, since this is your amazing
discovery, after all, but he was wrong in saying
that ln(A) can be defined by using a power series
(except under certain conditions. Can you tell us
_when_ ln(A) _can_ be defined using a power series,
and can you tell us what the definition of ln(A)
is for A not satisfying that condition? If you do
stumble on the definition you'll find that there
are many different choices for ln(A); which one
did you mean?)
>and before objections are made , i said det =/= [0;1]
>
>
>>
>> both exp and ln
>> may be defined on square matrices
>> using the power series
>> (though there may be convergence to consider)
>
>perhaps i should try to sell a book too , like david.
You should definitely do that. Let us know when you've
found a publisher.
>yeah , ill sell david ullrich a book about subjects like :
>
>continu iterations ( gamma , Barnes G , tetration , moebius transforms etc )
>
>matrix powers ( A^C )
>
>polysigned ( with credit to timothy )
>
>large cardinal axioms ( it was strange nobody noticed these missing in the ' disproofs ' of TST and aleph_aleph_0 is max , they assumed the large cardinals could be proven to exist just with ZF ... )
>
>
>>
>> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
>> galathaea: prankster, fablist, magician, liar
>
>regards
>
>tommy1729
David C. Ullrich
David R Tribble
>> So tell me: What in the world
>> do you think that A^C is, if A and C are 2x2 matrices.
>> What _is_ "A to the power C"?
>
galathaea wrote :
>> wouldn't that just be exp(C ln(A))?
>
amy666 wrote:
> yep thats it.
So to break this amazing new discovery down into simpler parts,
what is exp(I), where I is the usual 2x2 identity matrix?
Given Z as the zero matrix, is exp(Z) = I?
We'll next ask, of course, what ln(I) is, but first things first...
-drt
ge...@math.mq.edu.au
> David C. Ullrich wrote:
> >> So tell me: What in the world
> >> do you think that A^C is, if A and C are 2x2 matrices.
> >> What _is_ "A to the power C"?
>
> galathaea wrote :
>
> >> wouldn't that just be exp(C ln(A))?
>
> amy666 wrote:
> > yep thats it.
>
> So to break this amazing new discovery down into simpler parts,
> what is exp(I), where I is the usual 2x2 identity matrix?
>
> Given Z as the zero matrix, is exp(Z) = I?
Exponentiating matrices is no new discovery, rather it's quite
standard.
exp(A) can be defined for any square matrix A by the usual power
series
for the exponential function, viz.,
exp(A) = I + A + (A^2)/2 + (A^3)/6 + ...
This always converges.
--
GM
David C. Ullrich
I considered saying that, but decided it would be more interesting
to see what Timmy had to say on the question.
Of course it will still be interesting to see what he has to
say about the definition of ln(A); if he can actually give
a coherent definition of _that_ it will be something.
Pete Klimek
news:gerry-8B3594....@sunb.ocs.mq.edu.au...
> In any event, my suggestion that commuting is the same as simultaneous
> Jordaning is incorrect. The matrices A and B given by
>
> 1 1 0
> 0 1 0
> 0 0 2
>
> and
>
> 3 0 0
> 0 4 1
> 0 0 4
>
> are both in Jordan form (so a fortiori they are simultaneously
> Jordanable), they even have the same Jordan block structure,
> but they do not commute. I give up. I don't know what theorem,
> if any, characterizes commuting matrices in terms of simultaneous
> somethingizability.
>
> --
> Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)
It appears to me that square matrices commute iff they are simultaneously
diagonalizable. The following pdf file gives what seems to me to be a proof:
http://www.math.uri.edu/~quinn/web/mth513_theorem1312.pdf
Also, this result is given in a series of exercises in Friedberg, Insel and
Spence's Linear Algebra, p. 282 (ex. 18) and pp. 324-325 (exs. 23-25).
Pete Klimek
Timothy Murphy
> It appears to me that square matrices commute iff they are simultaneously
> diagonalizable. The following pdf file gives what seems to me to be a
> proof:
What if B = C is not diagonalizable?
Pete Klimek
news:GwIVk.838$jZ1...@flpi144.ffdc.sbc.com...
Sorry, the result should be: diagonalizable square matrices commute iff they
are simultaneously
diagonalizable.
Pete Klimek
galathaea
> >galathaea wrote :
> >> "David C. Ullrich" <dullr...@sprynet.com> wrote:
>
> >> > So tell me: What in the world
> >> > do you think that A^C is, if A and C are 2x2
> >> > matrices.
>
> >> > What _is_ "A to the power C"?
>
> >> wouldn't that just be
>
> >> exp(C ln(A))?
>
> >yep thats it.
>
> That's funny - you need someone else to say what you meant.
>
> Why is it that and not, say, exp(ln(A) C)?
>
> And exactly what do you mean by ln(A)? I didn't
> bother asking galathea, since this is your amazing
> discovery, after all, but he was wrong in saying
> that ln(A) can be defined by using a power series
> (except under certain conditions. Can you tell us
> _when_ ln(A) _can_ be defined using a power series,
> and can you tell us what the definition of ln(A)
> is for A not satisfying that condition? If you do
> stumble on the definition you'll find that there
> are many different choices for ln(A); which one
> did you mean?)
if you wanted a 1-on-1 conversation with tommy
email would be more appropriate than usenet
i think you have an error in your post
the correct thing to say is:
galathaea was _right_ in saying
that ln(A) could be defined using a power series
and even pointed out that you may need to consider convergence
depending on the particular matrix
of course
a lot of this begs some questions
if you don't know about matrix exponentiation
then it indicates you probably haven't read any
intro texts on lie algebras
(which almost all contain a good mention
including campbell-baker-hausdorff
and the geometric and arithmetic meanings)
and if you haven't read intro lie algebra texts
then your new book probably doesn't go into
solutions of differential equations
and the associated germs and such
that's okay
complex analysis often waits to explore those issues
( many don't want to have to build the whole fibration theory
foundation )
but it means your coverage of monodromy
is bound to be pretty superficial
generating trajectories won't be given a clear differential foundation
that's fine
usually they call that complex differential topology
or something similar
i know
not quite the same target audience
oh
and i see that you are now playing off my alleged error
as a challenge to tommy
which you think will hide your initial challenge
in a well-i-had-a-more-subtle-point move
if i was more bad hearted
i might point out domination patterns
and connect them to capabilities as a teacher
in ways that might subvert the intellectual authority of your book
but don't worry
i wouldn't actually support any of those horribly offensive positions
and i hope you don't also just assume i'm horribly wrong
particularly when it is an area i've pursued in some detail
(specifically in my generalised trigonometry
where the operation generalises
what happens on the 2d rotation matrix)
and maybe
along the way
you can stop acting like a little child with tommy
and start acting like a teacher
i hear that's what you do
(you've been corrected before
about another error you seem to like to continue with)
David C. Ullrich
Really? Exactly how does that go.
> and even pointed out that you may need to consider convergence
> depending on the particular matrix
>
>of course
> a lot of this begs some questions
>
>if you don't know about matrix exponentiation
Why would you conclude that? Of course there's
no problem defining the exponential of a matrix;
I haven't said anything to the contrary.
Now explain exactly how I use power series to
define ln(A).
Fabulous. Then explaining how to use power series to
define ln(A) should be no problem.
> (specifically in my generalised trigonometry
> where the operation generalises
> what happens on the 2d rotation matrix)
>
>and maybe
> along the way
>you can stop acting like a little child with tommy
>and start acting like a teacher
>
>i hear that's what you do
>
>(you've been corrected before
> about another error you seem to like to continue with)
>
>-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
>galathaea: prankster, fablist, magician, liar
David C. Ullrich
Mariano Suárez-Alvarez
Sure. The fun starts when you consider non-diagonalizable
matrices ;-)
-- m
alainv...@gmail.com
>
> - Afficher le texte des messages précédents -
Bonsoir,
"The fun starts when you consider non-diagonalizable
matrices "
I gave an example of commuting matrices without caring about
diagonalizability .
Am I right to think that if there is a n degree non null
polynomial p for a given matrix A such as p(A)=0 then things like
exp(A) are also n degree polynomials,
Alain
Mariano Suárez-Alvarez
For *every* matrix A there is a degree n polynomial p
such that p(A)=0. Google for "Cayley-Hamilton theorem"...
-- m
galathaea
> On Fri, 21 Nov 2008 21:17:09 -0800 (PST), galathaea
> >if you don't know about matrix exponentiation
>
> Why would you conclude that? Of course there's
> no problem defining the exponential of a matrix;
> I haven't said anything to the contrary.
well
someone who wants to make fun of another
for writing
A^C
for A and C matrices
doesn't display an understanding of matrix exponentiation
if you really did know this has meaning
then i'd expect your first reaction
would not be to make fun of someone
> Now explain exactly how I use power series to
> define ln(A).
i don't think you do
but others would just use
oo
--- j
\ (A - I)
ln(A) = / --------
--- j
j=1
just like you would for the natural ln over reals
as long as that matrix (A - I)
has flat square norm < 1
(iow: the sum of the squares of all it's entries)
then the matrix converges
much as one sees with the complex series
if the matrix has certain useful relations
like certain forms of it's cayley-hamilton
then the series might be finitely tractable
that's essentially the hack
my control theory teacher taught
and of course
once started with a meromorphic neighborhood
analytic continuation that simply avoids the pole
extends the definition everywhere else
(and shows it's multivalued nature
exactly like the original)
but now
once again
if this is so hard for you to see
how do you cover series definitions
and analytic continuation
in your book?
do you do it in a way
that doesn't make sense for matrices?
i'm saying all this about your book
because you still haven't taken back
your error about my position
it's a silly stand
but i love to properly corrected
and hate to be falsely corrected
particularly by someone already on teasing kick
so i'm just pointing out
if you really can't see any of it
it is not saying great things about your book
David C. Ullrich
<gala...@gmail.com> wrote:
>On Nov 22, 6:05 am, David C. Ullrich <dullr...@sprynet.com> wrote:
>> On Fri, 21 Nov 2008 21:17:09 -0800 (PST), galathaea
>
>> >if you don't know about matrix exponentiation
>>
>> Why would you conclude that? Of course there's
>> no problem defining the exponential of a matrix;
>> I haven't said anything to the contrary.
>
>well
> someone who wants to make fun of another
> for writing
>
> A^C
> for A and C matrices
>
>doesn't display an understanding of matrix exponentiation
I asked Timmy for the definition, confident that
he had no idea what he was talking about.
>if you really did know this has meaning
> then i'd expect your first reaction
> would not be to make fun of someone
You're saying that, for example,
exp(C ln(A)) is _the_ definition, and not,
for example, exp(ln(A) C)?
>> Now explain exactly how I use power series to
>> define ln(A).
>
>i don't think you do
Fascinating. So I was _right_ when I said you
were wrong about that, and you were wrong when
you said I was wrong about saying you were wrong
about that, right?
Got it.
>but others would just use
>
> oo
> --- j
> \ (A - I)
>ln(A) = / --------
> --- j
> j=1
>
>just like you would for the natural ln over reals
Erm, that's certainly not what _I_ would use
for the _definition_.
>as long as that matrix (A - I)
> has flat square norm < 1
> (iow: the sum of the squares of all it's entries)
>then the matrix converges
Yes, for _some_ matrices that works.
In fact for a much larger class of matrices
then you seem to realize, but never mind
that.
For other matrices of course you could use
other power series. But it's easy to give an
example of a matrix for which _no_ power
series works. That is, a matrix A such that there
does not exist z_0 in C and a sequence c_n such
that sum c_n (z-z_0)^n converges to ln(z)
in some disk in the plane and sum c_n (A - z_0I)^n
onverges.
>much as one sees with the complex series
>
>if the matrix has certain useful relations
> like certain forms of it's cayley-hamilton
>then the series might be finitely tractable
>
>that's essentially the hack
> my control theory teacher taught
>
>and of course
> once started with a meromorphic neighborhood
>analytic continuation that simply avoids the pole
>extends the definition everywhere else
>(and shows it's multivalued nature
> exactly like the original)
Explain to us how that continuation works
for _matrices_.
>but now
> once again
>if this is so hard for you to see
>how do you cover series definitions
> and analytic continuation
>in your book?
You haven't said anything I don't know,
except of course for your claim that
(with no restrictions stated on A except
that its determinant is not 0 or 1) you
can define ln(A) by a power series.
Which of course is false, so I'm glad I
don't "know" it.
>do you do it in a way
> that doesn't make sense for matrices?
>
>i'm saying all this about your book
> because you still haven't taken back
> your error about my position
Fascinating. You've already _agreed_ with
my supposed "error" about your error.
>it's a silly stand
> but i love to properly corrected
> and hate to be falsely corrected
> particularly by someone already on teasing kick
>
>so i'm just pointing out
> if you really can't see any of it
> it is not saying great things about your book
Giggle. I think I'll talk to the publisher, and add
something to the cover of the next edition specifying
that "galathea" and "amy666" have both expressed
a lot of skepticism about the quality of the text
(without seeing it, or course). Should be great
for sales.
Maybe I can get JSH in on this too.
>-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
>galathaea: prankster, fablist, magician, liar
David C. Ullrich
galathaea
dcu:
> g:
> >so i'm just pointing out
> > if you really can't see any of it
> > it is not saying great things about your book
>
> Giggle. I think I'll talk to the publisher, and add
> something to the cover of the next edition specifying
> that "galathea" and "amy666" have both expressed
> a lot of skepticism about the quality of the text
> (without seeing it, or course). Should be great
> for sales.
no
you completely misunderstand me
i am saying
your appearance is often aggressive and domineering
you look for flaws
and then use it intimidatingly
younger students
who are always the ones with the most flaws
if
in your book
instead of pointing to ways of extending a definition
and pointing the path to generalities
you treat the reader with scorn
trying to trick the reader into some flaw
then it might not be a good book
but i don't have any knowledge that your book does that
which makes me wonder why you do that on usenet
and there is a very real sense in which
you are representin' your book
look
if you know about the algebraic study
of extensions of exponentiation to more general structures
then post some cool ramifications of the shit
make it interesting
but don't discourage others
and don't belittle the knowledge
because tommy does know about them now
whether or not you choose to believe it yet
did tommy know about it
only five minutes before he posted about it?
maybe he only really knew about them
five minutes after i posted my response
(which i still think has
the funniest hidden joke of the century)
or maybe he has been hatching his ideas about them
secretly for several years
perfecting the every nuance of his understanding
he knows about them now
that is clear
what he does with them is anybody's guess
On Nov 22, 2:15 pm, David C. Ullrich <dullr...@sprynet.com> wrote:
> On Sat, 22 Nov 2008 11:54:40 -0800 (PST), galathaea
>
>
>
> <galath...@gmail.com> wrote:
> >On Nov 22, 6:05 am, David C. Ullrich <dullr...@sprynet.com> wrote:
> >> On Fri, 21 Nov 2008 21:17:09 -0800 (PST), galathaea
>
> >> >if you don't know about matrix exponentiation
>
> >> Why would you conclude that? Of course there's
> >> no problem defining the exponential of a matrix;
> >> I haven't said anything to the contrary.
>
> >well
> > someone who wants to make fun of another
> > for writing
>
> > A^C
> > for A and C matrices
>
> >doesn't display an understanding of matrix exponentiation
>
> I asked Timmy for the definition, confident that
> he had no idea what he was talking about.
the teacher is the one who takes the job of teaching
and the student takes the task of learning
if you were confident of the relationship
you seemed to jump to the wrong task
> >if you really did know this has meaning
> > then i'd expect your first reaction
> > would not be to make fun of someone
>
> You're saying that, for example,
> exp(C ln(A)) is _the_ definition, and not,
> for example, exp(ln(A) C)?
that is a good question
the ln form i am most comfortable with
is the one that eats operators from the right
A ln(B) = ln(B ^ A)
whose inverse would then map to the argument
but there are dual theories
identically opposite in their ways
and lots of really cool structure
to teach a student
> >> Now explain exactly how I use power series to
> >> define ln(A).
>
> >i don't think you do
>
> Fascinating. So I was _right_ when I said you
> were wrong about that, and you were wrong when
> you said I was wrong about saying you were wrong
> about that, right?
>
> Got it.
> >but others would just use
>
> > oo
> > --- j
> > \ (A - I)
> >ln(A) = / --------
> > --- j
> > j=1
>
> >just like you would for the natural ln over reals
>
> Erm, that's certainly not what _I_ would use
> for the _definition_.
why not?
it's a natural start for a definition
from the purely formal algebraics
in complex matrices
the exponent of the zero matrix is the identity
this is the only fully rational point on the graph
the logarithm of the identity
is the zero matrix
(along with a countable set of others)
so these are obvious points to build a formal series on
the series has a positive radius of convergent
so we at least know we are talking about something functionlike
at least on one neighborhood
looking around
we only see one major singularity
so the manifold may be analytically continued
and so starting on that neighborhood
seems to be a pretty solid starting point
using all the basic tools of analysis
that gets us what we want
formally
the composition works to make sense of the inverse relation
> >as long as that matrix (A - I)
> > has flat square norm < 1
> > (iow: the sum of the squares of all it's entries)
> >then the matrix converges
>
> Yes, for _some_ matrices that works.
> In fact for a much larger class of matrices
> then you seem to realize, but never mind
> that.
if you mean the matrices on the boundary
except for the single singularity
then yeah
there are more
you should try teaching that
i'm sure people would be interested
> For other matrices of course you could use
> other power series. But it's easy to give an
> example of a matrix for which _no_ power
> series works. That is, a matrix A such that there
> does not exist z_0 in C and a sequence c_n such
> that sum c_n (z-z_0)^n converges to ln(z)
> in some disk in the plane and sum c_n (A - z_0I)^n
> converges.
there is a nonremovable logarithmic singularity
i am sure students would love to know more
> >much as one sees with the complex series
>
> >if the matrix has certain useful relations
> > like certain forms of it's cayley-hamilton
> >then the series might be finitely tractable
>
> >that's essentially the hack
> > my control theory teacher taught
>
> >and of course
> > once started with a meromorphic neighborhood
> >analytic continuation that simply avoids the pole
> >extends the definition everywhere else
> >(and shows it's multivalued nature
> > exactly like the original)
>
> Explain to us how that continuation works
> for _matrices_.
when you say things like that
you really should think about your representin'
a metric on matrices used for neighborhoods of convergence
provides all the apparatus for the overlaps
which topologically layout continuation maps
i already gave one
> >but now
> > once again
> >if this is so hard for you to see
> >how do you cover series definitions
> > and analytic continuation
> >in your book?
>
> You haven't said anything I don't know,
> except of course for your claim that
> (with no restrictions stated on A except
> that its determinant is not 0 or 1) you
> can define ln(A) by a power series.
> Which of course is false, so I'm glad I
> don't "know" it.
i'm sure you have something that you can't wait to pull out
that will show how this language is all flawed
and you get to feel all happy about it
but the thing you have been fighting
even if you've already known it for years
and are only intending to attack something smaller
is whether it is possible to define A^C for matrices
and whether matrices can have logarithms
and whether it is valid to speak of power series
for this def
all of that is possible
despite your bickering
so
maybe it's time you pull your little technical quip out
and move on
because along the way you seem to be just discouraging
something that is well established
> >do you do it in a way
> > that doesn't make sense for matrices?
>
> >i'm saying all this about your book
> > because you still haven't taken back
> > your error about my position
>
> Fascinating. You've already _agreed_ with
> my supposed "error" about your error.
more clever ways to avoid teaching
> >it's a silly stand
> > but i love to properly corrected
> > and hate to be falsely corrected
> > particularly by someone already on teasing kick
>
> Maybe I can get JSH in on this too.
just stop trying to trip people
people trip enough on their own
if you know about something
and don't think someone else does
tell a tale
don't pull a tail
galathaea
(i see i was a bit hurried with the art)
oo
--- j
\ j (A - I)
ln(A) = / (-1) --------
Denis Feldmann
Nor would I ,as there is still a sign mistake in it :-)
David C. Ullrich
<gala...@gmail.com> wrote:
>
>dcu:
>> g:
>
>> >so i'm just pointing out
>> > if you really can't see any of it
>> > it is not saying great things about your book
>>
>> Giggle. I think I'll talk to the publisher, and add
>> something to the cover of the next edition specifying
>> that "galathea" and "amy666" have both expressed
>> a lot of skepticism about the quality of the text
>> (without seeing it, or course). Should be great
>> for sales.
>
>no
>
>you completely misunderstand me
>
>i am saying
> your appearance is often aggressive and domineering
>
>you look for flaws
> and then use it intimidatingly
Fascinating how we seem to have shifted the subject
from ln(A) to me. I wonder why that would be?
Oh, right: What you said was wrong, your sarcastic
correction to my statement that it was wrong was
wrong, and you can't simply admit it.
Giggle.
>younger students
> who are always the ones with the most flaws
>
>if
> in your book
> instead of pointing to ways of extending a definition
>and pointing the path to generalities
>you treat the reader with scorn
> trying to trick the reader into some flaw
Wow. How did you guess that that was the point
to the book? Amazing?
>then it might not be a good book
What? I thought that tricking the reader was the whole
point. I may have to rethink my approach...
Hint: You're making a fool of yourself with all this.
>but i don't have any knowledge that your book does that
>
>which makes me wonder why you do that on usenet
> and there is a very real sense in which
> you are representin' your book
>
>look
> if you know about the algebraic study
> of extensions of exponentiation
exponentiation? We've agreed there's no problem
with exp here, the problem is with ln.
>to more general structures
>then post some cool ramifications of the shit
>
>make it interesting
Exquisitely fascinating. Just as with Timmy, you're
unable to answer questions clarifying things you say.
You say something vague about extending the definition
from ||A - I|| < 1 to other matrices by analytic continuation,
I ask exactly how you do that, and instead of explaining
you tell _me_ to explain things that _you_ have asserted.
Fascinating.
>but don't discourage others
>
>and don't belittle the knowledge
>
>because tommy does know about them now
> whether or not you choose to believe it yet
>
>did tommy know about it
> only five minutes before he posted about it?
>
>maybe he only really knew about them
> five minutes after i posted my response
>(which i still think has
> the funniest hidden joke of the century)
>
>or maybe he has been hatching his ideas about them
> secretly for several years
>perfecting the every nuance of his understanding
>
>he knows about them now
>
>that is clear
What's clear is that he had no idea what he actually
meant when he mentioned A^C. That would be clear
to anyone who'd read his previous posts on various
subjects - it's much more clear from the fact that
he didn't reply when I asked for the definition,
just saying you were right when you suggested
he meant exp(C ln(A)). Also from the fact that
he hasn't answered any of the several questions
I asked him about that.
Nor have you, by the way. For example, why is
it exp(C ln(A)) instead of exp(ln(A) C)?
The idea that thoughts about how one should deal
with students has something to do with how one
should deal with Timmy is ridiculous, by the way.
Students don't insist that they understand mathematics
(including areas of math that they really know nothing
at all about) better than all the mathematicians
on the planet. Yes, if I ever had a student who
consistently acted the way Timmy does things
would everntually become unpleasant. That
has no relevance to how I treat actual students.
David C. Ullrich
Denis Feldmann
Counter-hint : what makes you believe his/her signature is not serious ?
galathaea
> On Sat, 22 Nov 2008 20:13:14 -0800 (PST), galathaea
>
>
> >dcu:
> >> g:
>
> >> >so i'm just pointing out
> >> > if you really can't see any of it
> >> > it is not saying great things about your book
>
> >> Giggle. I think I'll talk to the publisher, and add
> >> something to the cover of the next edition specifying
> >> that "galathea" and "amy666" have both expressed
> >> a lot of skepticism about the quality of the text
> >> (without seeing it, or course). Should be great
> >> for sales.
>
> >no
>
> >you completely misunderstand me
>
> >i am saying
> > your appearance is often aggressive and domineering
>
> >you look for flaws
> > and then use it intimidatingly
>
> Fascinating how we seem to have shifted the subject
> from ln(A) to me. I wonder why that would be?
> Oh, right: What you said was wrong, your sarcastic
> correction to my statement that it was wrong was
> wrong, and you can't simply admit it.
>
> Giggle.
i'll admit any wrong doing you point out
i do it every time i screw up around here
and it is not something i am embarrassed about
so your point is kind of odd
do you think A^C is meaningless or impossible?
which of my points are you jumping on your hands
waiting to point out?
if you just do it
instead of trying to use it pawn your way out
of being so discouraging to the A^C notion
then i would learn faster
(and everyone can see whatever petty point you are now trying to make
as opposed to whatever petty point you were originally trying to
make)
just fuckin' say what you mean
david
instead of giggling awkwardly
> >younger students
> > who are always the ones with the most flaws
>
> >if
> > in your book
> > instead of pointing to ways of extending a definition
> >and pointing the path to generalities
> >you treat the reader with scorn
> > trying to trick the reader into some flaw
>
> Wow. How did you guess that that was the point
> to the book? Amazing?
i didn't guess that
i said that's how you behave on usenet
_if_ you also behaved that badly in your book
_then_ your book is probably bad
> >then it might not be a good book
>
> What? I thought that tricking the reader was the whole
> point. I may have to rethink my approach...
>
> Hint: You're making a fool of yourself with all this.
hint: you still have not answered
why you are like that in usenet
in fact: you are still acting like it
instead of giving some kind of exposition
you are looking for something wrong in what i have said
where i came in simple to point out
despite your skepticism
A^C has a definition
with much mathematical structure
> >but i don't have any knowledge that your book does that
>
> >which makes me wonder why you do that on usenet
> > and there is a very real sense in which
> > you are representin' your book
>
> >look
> > if you know about the algebraic study
> > of extensions of exponentiation
>
> exponentiation? We've agreed there's no problem
> with exp here, the problem is with ln.
>
> >to more general structures
> >then post some cool ramifications of the shit
>
> >make it interesting
>
> Exquisitely fascinating. Just as with Timmy, you're
> unable to answer questions clarifying things you say.
> You say something vague about extending the definition
> from ||A - I|| < 1 to other matrices by analytic continuation,
> I ask exactly how you do that, and instead of explaining
> you tell _me_ to explain things that _you_ have asserted.
tell me what i have failed to clarify
just fuckin' do it
instead of feeling all that glee you get
from experiencing the flaws of others
just fuckin' come out with it
you want a better explanation of matrix analytic continuation?
i can give all the steps needed
to describe a monodromy theorem analogue for matrices
is that what you want?
are you saying
as a professor of complex analysis
you need to be hand-held and walked through matrix ca?
why do you feel such a need to delight in other's ignorances?
i've read a lot of tommy's posts
it is clear to me that he at least reads advanced material
and is interested in owning his own understanding
to me
that indicates someone self-motivated to a large understanding
i don't think he's quite developed enough
to make one of those great discoveries hiding out there
not without some good practice of the tools
but he is at least learning his way around
and ready to challenge with bold generalisations
he'll be making a lot of mistakes until then
but i also have little doubt he will get there
your goal seems to be to discourage him from getting there
> Nor have you, by the way. For example, why is
> it exp(C ln(A)) instead of exp(ln(A) C)?
i mentioned the form i am comfortable with
and the duality in the theory
in my last post
just read for comprehension
instead of hunting for errors for once
> The idea that thoughts about how one should deal
> with students has something to do with how one
> should deal with Timmy is ridiculous, by the way.
> Students don't insist that they understand mathematics
> (including areas of math that they really know nothing
> at all about) better than all the mathematicians
> on the planet. Yes, if I ever had a student who
> consistently acted the way Timmy does things
> would everntually become unpleasant. That
> has no relevance to how I treat actual students.
and when i come
asking you to stop being a prick
and stop pretending there are insurmountable hurdles to the theory
and just be a teacher and fuckin' teach
your continuance of the crypto-aggression means?
if you were a teacher of mine
i would hope when i came up to you and asked about matrix
exponentiation
and show you some papers where i've sketched out relations
you'd tell me that
- well it's pretty established already
- so here's some good references to learn from
- and
like in standard exponents
you have to be aware of multivaluedness
- but otherwise
yeah it's a cool structure
with a lot of geometric and arithmetic importance
i've certainly started sketching
what i mean by it
and your behavior has not gotten better
so...
you going to go another post
where you continue to just vaguely suggest there was an error
somewhere
that you were deeply concerned about in the whole A^C enterprise
but it's still too early to let it spill
(as you savor the deliciousness of the immanent giggles)?
or you gonna grow up a little
and actually discuss A^C?
and are you really gonna try to make me step you through
matrix analytic continuation
starting with the convergence metric i already mentioned
and working through all the standard details
on paths in analytic regions?
if so on this latter part
you may have to wait a few days
which may be nice for your luxuriating in deliciousness
but it will also be a lot of time for other readers to ask
"hey, what does this complex anlysis prof
have against matrix analytic continuation"
it will be several days of you digging yourself deeper into a position
that many could easily look up papers online
(since it is extremely common for physicists to use
there's bound to be an undergrad worksheet online or something)
is that how you want this to go?
you keep dropping hints
like you know i'm ignorant somewhere
just like you know tommy's ignorant somewhere
are you really prepared to draw a line and say
this! (A^C or matrix analytic continuation or ...)
this is what i challenge!
or are you just gonna sit back
try to give some a fear that
oh my god
don't tread there!
david knows something and i think he's serious...
you claimed i'm being vague
but i look at this subthread
and i see i'm the only one who's mentioned an interpretation
you've been sitting back
you are the one being vague and not backing yourself up
Gerry Myerson
<ba01237e-d30b-410f...@h5g2000yqh.googlegroups.com>,
Mariano Suárez-Alvarez <mariano.su...@gmail.com> wrote:
I think you've missed the point of the (awkwardly-phrased)
question. Perhaps the question was meant to go like this:
if the minimal polynomial for A is of degree n, then can exp(A)
be expressed as a polynomial in A of degree n.
If A satisfies a polynomial of degree n, then every power of A
can be expressed as a linear combination of I, A, A^2, ..., A^(n-1),
so (modulo some hand-waving about taking limits) exp(A) must be
a polynomial of degree at most n - 1 in A.
amy666
dont worry , he cant trip me :)
he's trippin himself with showing his ignorance of the meaning of A ^ C for matrices and matrix exponentiation in general.
just as he was while doubting continu iterations on the real line.
and the fact that david doesnt know about matrix exponentiation , is a bad omen for his book ...
regards
tommy1729
amy666
' bla bla bla nothing about matrix exponentiation or matrices that commute ' + ' childish behaviour to hide his ignorance '
ok david
im sick of you telling me to prove myself , while at the same time you show the ignorance of e.g. matrix exponentiation.
you prove yourself this time , since i might have actually solved the problem of the OP , while you are still trying to figure out exponentiation of matrices and log branches.
lets turn the tables.
you be the student and give me a counterexample to
my post made on 19/11/08 in this thread.
should be easy for you not ??
tommy1729
Pete Klimek
news:_2JVk.27493$j7.4...@news.indigo.ie...
Quite correct. I amended the above statement in a later post
("diagonalizable square matrices commute iff they are simultaneously
diagonalizable") and acknowledge that the difficulty arises when the
matrices are not diagonalizable.
Pete Klimek
~Glynne
The meaning of M^N is an interesting question which I have pondered
for
some time. In your flamewar with David you have (both) glossed over
an
import issue.
Given
M = an mxm matrix
N = an nxn matrix
You asserted that:
(1) log(M^N) = N*log(M)
(2) M^N = exp(N*log(M))
David then pointed out that one could equally assert that:
(1') log(M^N) = log(M)*N
(2') M^N = exp(log(M)*N)
but you both missed the larger point -- that these cannot use normal
matrix multiplication.
Let's examine 2 cases for which we "know" the result.
Given
s = a scalar
M = an mxm matrix
We know that:
M^s = an mxm matrix
s^M = an mxm matrix
From these 2 cases, it appears that the exponentiation operator
"works"
for square matrices of different dimensions -- if you consider
scalars
to be 1x1 matrices -- and the result is a matrix whose dimensions are
the product of the dimensions of the argument matrices.
But what kind of product can be used with a 1x1 and mxm matrix?
Simply putting a kronecker product into eqn (1) or (2) is intriguing;
a direct/tensor product is less so.
A symmetrized kronecker product
N # log(M) = [log(M)*N + N*log(M)]/2
would address David's ordering issue.
Such a definition would also need to define log(M) very carefully
...as David has pointed out.
But, in a dimensional sense, M^N needs be a kronecker-type
operation.
~Glynne
galathaea
the particular operation david asked about
was for both M and N to be the same size
(2x2)
in this case
the operations are
ln(m): M(2)* --> M(2)
m . n: M(2) x M(2) --> M(2)
exp(m): M(2) --> M(2)
and so normal multiplication works fine
that's all i was trying to define
if i had tried to define matrix operations
for square matrices of different sizes
i would probably start with multiplication
and only then describe exponentiation in relation
but kronecker is definitely one possibility
and you are right that ordering can be a useful operation
which may make some formulae more tractable
this is abused a lot in quantum electrodynamics
but you will want to investigate
both symmetric and antisymmetric behavior
or at least their relationship
to get the full theory
an interesting way to measure a slightly different ordering
interaction
is generalising the exponential relations
like generalised baker-campbell-hausdorff
Y Z Y ln(X) Z ln(X)
X X = e e
Y ln(X) + Z ln(X) + 1/2 [Y ln(X), Z ln(X)] + 1/12...
= e
Y + Z + 1/2 [Y, Z] + 1/12 [Y, [Y, Z]] - 1/12...
= X
and similarly
X X
Y Z = (get to use the logarithmic product form on this one!)
galathaea
notice also that all matrix relations in this thread
are of the same size
but
just to give an idea
of how i have used exponentiation in the past
i will repeat a generalised trigonometric equation
i discovered some time back
define the circulant matrix
|0 1 0 ... 0|
|0 0 1 ... 0|
|0 0 0 ... 0|
W = |. . . . .|
n |. . . . .|
|. . . . .|
|0 0 0 ... 1|
|1 0 0 ... 0|
then
W x
n
e
is equal to
| |n-1 x |0 x |1 x |n-2 x |
| |n e |n e |n e ... |n e |
| |
| |n-2 x |n-1 x |0 x |n-3 x |
| |n e |n e |n e ... |n e |
| ... |
(you get the idea)
where the
|m x
|n e
are the (m, n)-multisection
generalised (hyperbolic) trigonometrics
a similar form for generalised circular trigs
if you put a -1 somewhere for inversion
(symmetry says the bottom left corner)
in fact
this was one of the first relations i derived
that directly described multisection
in the language of matrices
and is one of my results i am most proud of
alainv...@gmail.com
To Everybody,
I just wish to tell you :
1)The example of commutation I've given was built from
two different polynomials C =p1(A) , B=p2(A) ,
noboby explain me the link with simutanously diagonalizable matrices;
2) Some shown examples were 'roots' of null matrices
or simple combinations thereof ,
3) May we consider ||A||^ 0 = Id identity ?
Alain
David C. Ullrich
wrote:
>David C Ullrich wrote :
>
>' bla bla bla nothing about matrix exponentiation or matrices that commute ' + ' childish behaviour to hide his ignorance '
>
>
>
>ok david
>
>im sick of you telling me to prove myself , while at the same time you show the ignorance of e.g. matrix exponentiation.
>
>you prove yourself this time , since i might have actually solved the problem of the OP ,
"might" have. Right. Never mind the fact that you have no evidence
whatever for the idea that what you posted actually gave a solution,
in fact what you posted is meaningless.
>while you are still trying to figure out exponentiation of matrices and log branches.
>
>
>lets turn the tables.
>
>you be the student and give me a counterexample to
>
>my post made on 19/11/08 in this thread.
>
>should be easy for you not ??
That's impossible until you explain what you mean. You said
this:
"
i believe matrix A and B commute if
- assuming they have abs different from 1 or 0 -
- assuming both are square matrices -
if A^C = B for some square matrix C
where C satisfies C D = D C for any square matrix D.
- assuming all matrices are of the same size of course -"
When I asked what you meant by A^C you didn't reply -
then you said yes when g said it was exp(C ln(A)).
But you haven't said what you mean by ln(A).
(That's a separate question from the question of
proving the existence of ln(A), which isn't hard,
although you've ignored the question and g has
refused to do, instead just replying to corrections
with insults and complaints.) In fact A has many
different logarithms - which one are you referring to?
You also need to clarify what you mean by
"C satisfies C D = D C for any square matrix D";
do you mean that CD = DC for every D or that
there exists D such that CD = DC. (Hint: If you
mean the second that says nothing whatever
about C. If you mean the first that does put
a severe restriction on C - of course you don't
know what it actually does say about C or
you would not have stated the condition in such
a clumsy way).
>
>tommy1729
Chip Eastham
If PAP^-1 is diagonal, and C = p(A) is a polynomial
in A, then PCP^-1 is also diagonal. All polynomials
in A are simultaneously diagonalizable if A is
diagonalizable (similar to a diagonal matrix).
> 2) Some shown examples were 'roots' of null matrices
> or simple combinations thereof ,
>
> 3) May we consider ||A||^ 0 = Id identity ?
>
> Alain
When we apply a polynomial to a matrix, the
convention is A^0 = I, the identity matrix.
Hence the constant term of the polynomial
becomes that multiple of the identity matrix.
[No need to take the norm of A here, ||A||,
which would result in a scalar.]
regards, chip
galathaea
> When I asked what you meant by A^C you didn't reply -
> then you said yes when g said it was exp(C ln(A)).
why does someone have to reply right away?
why would you expect tommy would get to your question first?
it seems to me
you are interpreting the sequence of events
purposely negatively
> But you haven't said what you mean by ln(A).
> (That's a separate question from the question of
> proving the existence of ln(A), which isn't hard,
> although you've ignored the question and g has
> refused to do, instead just replying to corrections
> with insults and complaints.) In fact A has many
> different logarithms - which one are you referring to?
i haven't refused anything
i'm not sure why you would even say that
since i've asked what you wanted
and you hadn't yet replied
now it looks like you want existence
which is simple once you know the series converges in an region
really
ullrich
you are one fucked up individual
Bill
>
> really
> ullrich
> ...
David Ullrich doesn't need me to stick up for him, but he's a pillar of
this forum. He's a demonstrated himself to be an impressive scholar,
and he's his charitable with his time and energy.
In comparison, I don't recognize your name...
galathaea
of course
it would be important to point out
that such a digression is purely an avoidance mechanism
meant to quench some cognitive dissonance
that ad hominems still do not answer
what david is trying to imply is wrong with the idea
(and that his recent post seemed to imply his issue was existence
but that he also in the same breath seemed to say
that wasn't really his issue)
but
if you want to compare achievements
we can do that
we can compare the achievements of myself
self-taught in mathematics
with only a very few number of undergrad math courses
who grew up extremely poor
and spent much of my money on books
often to the point of going without food
and that of david c ullrich
with his degrees and professorship
i think such a comparison would be highly telling
of his approach to discouraging investigation
which he has shown numerous times on the newsgroups
(and which there are a good deal of past threads
solely about ullrich's uglies)
we can start with his results in harmonic theory
in comparison to my generalised trigonometry
maybe you'd like to include your own results
bill?
i mean
since you brought up the idea
of comparing contributions
maybe you'd like to join too?
galathaea
or maybe
if the whole comparison thing is a bit too aggressive
maybe you'd like to explain what you think ullrich's point here is
so far
he has called me wrong several times
but has yet to add any substance himself
or justify his position
and has now turned to trying to play it off
as if i am refusing to do something
what do you think the point of that would be?
he slyly adds masculine referents
which he has been corrected on before
why do you think he tries to belittle like that?
how could any of this be taken
in a way that makes ullrich look good?
what worldview excuses his behavior here?
i am not in a mood that sees these things easily
but if you have anything that shows him in a better light
feel free to post it
on my end at least
he could really use some help in stating his case
because i am not someone who take belittlement well...
Rotwang
>
> but
>
> if you want to compare achievements
> we can do that
>
> we can compare the achievements of myself
> self-taught in mathematics
> with only a very few number of undergrad math courses
> who grew up extremely poor
> and spent much of my money on books
> often to the point of going without food
> and that of david c ullrich
> with his degrees and professorship
>
> i think such a comparison would be highly telling
> of his approach to discouraging investigation
> which he has shown numerous times on the newsgroups
Oh, bullshit. Utter, utter bullshit. I also taught myself what little
I know about mathematics, and I have received nothing but help from
David with my own investigations. Why do you suppose that is? Perhaps
it's because I don't post meaningless nonsense and then question
people's competence when they aren't able to guess what I would have
said if I were able to string a coherent thought together. Perhaps
it's because I don't post statements which are outright false and then
pretend I meant something else when called on it, and then insult
people for having disagreed with the statement I never actually wrote.
Perhaps it's because, unlike some people, I present evidence of having
done enough actual studying on the topics I'm interested in to be able
to write stuff about those subjects which isn't complete garbage.
For all the times you've suggested that Tommy should read up on such-
and-such in a bid to make sense out of his rantings, do you have any
evidence that he's ever actually done so? If he has, it doesn't show.
> (and which there are a good deal of past threads
> solely about ullrich's uglies)
Yes, I've seen many threads in which Ullrich is involved in arguments
about his conduct. It's also been my judgement in /every single one/
of those threads that Ullrich was *right*. Whether he is being accused
of incompetence, plagiarism or racism, the charges levelled against
him are consistently without merit. Perhaps he suffers fools less
gladly that some people, but given how many fools there are around
here I don't blame him.
MoeBlee
> we can compare the achievements of myself
> self-taught in mathematics
> with only a very few number of undergrad math courses
> who grew up extremely poor
> and spent much of my money on books
> often to the point of going without food
> and that of david c ullrich
> with his degrees and professorship
Not to mention the sheer undaunted heroisim you evince each day as you
post despite the handicap of a broken keyboard that inserts random
indents each line. Mere moral weaklings would wither, but not you!
MoeBlee
galathaea
> On 25 Nov, 18:14, galathaea <galath...@gmail.com> wrote:
>
>
>
>
>
> > but
>
> > if you want to compare achievements
> > we can do that
>
> > we can compare the achievements of myself
> > self-taught in mathematics
> > with only a very few number of undergrad math courses
> > who grew up extremely poor
> > and spent much of my money on books
> > often to the point of going without food
> > and that of david c ullrich
> > with his degrees and professorship
>
> > i think such a comparison would be highly telling
> > of his approach to discouraging investigation
> > which he has shown numerous times on the newsgroups
>
> Oh, bullshit. Utter, utter bullshit. I also taught myself what little
> I know about mathematics, and I have received nothing but help from
> David with my own investigations. Why do you suppose that is? Perhaps
> it's because I don't post meaningless nonsense and then question
> people's competence when they aren't able to guess what I would have
> said if I were able to string a coherent thought together.
can you give an example of meaningless nonsense i have posted?
i will try to clear up any questions you may have
> Perhaps
> it's because I don't post statements which are outright false and then
> pretend I meant something else when called on it, and then insult
> people for having disagreed with the statement I never actually wrote.
if i have done this to you
i apologise right now
i would like a reference where i have done this
so i can learn from my mistakes
> Perhaps it's because, unlike some people, I present evidence of having
> done enough actual studying on the topics I'm interested in to be able
> to write stuff about those subjects which isn't complete garbage.
what evidence do i need to provide you?
photograph?
results?
i have posted many results...
which did you find in error?
> For all the times you've suggested that Tommy should read up on such-
> and-such in a bid to make sense out of his rantings, do you have any
> evidence that he's ever actually done so? If he has, it doesn't show.
yes
i think tommy needs to apply himself more
and i tell him that
and yes
i will do so aggressively if i have been aggressed
but still
tommy has a tendency to raise questions
that are legitimate and interesting
and some
like ullrich
are often immediately _and_incorrectly_ hostile
it is that immediacy
the kind that attacks legitimate mathematics in the process
that i find offensive
that is the bullshit
the utter utter bullshit
> > (and which there are a good deal of past threads
> > solely about ullrich's uglies)
>
> Yes, I've seen many threads in which Ullrich is involved in arguments
> about his conduct. It's also been my judgement in /every single one/
> of those threads that Ullrich was *right*. Whether he is being accused
> of incompetence, plagiarism or racism, the charges levelled against
> him are consistently without merit. Perhaps he suffers fools less
> gladly that some people, but given how many fools there are around
> here I don't blame him.
so what is ullrich's point here?
please be clear about it
since you've attacked me here too
saying i am unable to be clear
do you think it is meaningless to write A^C
for 2 square matrices A and C of the same size?
you say he is _always_ right
so this should be a good confirmation...
galathaea
still sore about my pointing out
your own chest-thumping re: predicativism and poincare?
i agree my communication is broken
i agree i am broken
i admit it in a heartbeat
even still
i do not hide around
waiting to attack someone on the first possible mistake
look at my first post in this thread
was there aggression there?
can anyone explain ullrich's issue here
instead of delighting in the battle?
if you can
you get to "defeat" me heroically on the battlefield
and can take the fame and fortune whereever it leads
i will even gladly bow humbly to my teacher
and post whatever self-effacing commentary is desired
come on
just do it
otherwise
what the fuck is wrong with you guys?
are you seriously supporting a poster's ability
to post substanceless innuendo
where the poster being attacked
is the one actually supplying any substance?
do you find that to be a good position to be in?
is it a dynamic you support?
galathaea
> please be clear about it
> since you've attacked me here too
> saying i am unable to be clear
i am most interested in this part
be as clear as absolutely possible
in explaining what this is all about
i didn't attack you
so far
several have jumped in to attack me
but no one has explained how it was proper
for ullrich to demean the idea of matrix exponentiation
and follow with several posts claiming i am wrong about something
without illustrating any errors
do you see how people like jsh
could get erroneous ideas about mathematicians?
you say ullrich doesn't suffer fools kindly
i don't like being a fool
it isn't something that i desire flaunting in front of everyone
a simple explanation seems like it might be worthwhile
i mean
you guys do that for james when he is really far gone
so if you'd just do it for me
maybe i could learn and stuff...
MoeBlee
> still sore about my pointing out
> your own chest-thumping re: predicativism and poincare?
I don't know what you're talking about. Perhaps you have me confused
with another poster?
> can anyone explain ullrich's issue here
> instead of delighting in the battle?
I may have all kinds of thoughts about Internet conversations, but my
last post was just, as I thought would be obvious, a bit of fun about
your seemingly self-serious "I was born in a log cabin and walked six
miles in the snow to school each day, uphill, both ways"-style plea.
MoeBlee
Rotwang
> On Nov 25, 11:54 am, Rotwang <sg...@hotmail.co.uk> wrote:
>
>
>
> > On 25 Nov, 18:14, galathaea <galath...@gmail.com> wrote:
>
> > > but
>
> > > if you want to compare achievements
> > > we can do that
>
> > > we can compare the achievements of myself
> > > self-taught in mathematics
> > > with only a very few number of undergrad math courses
> > > who grew up extremely poor
> > > and spent much of my money on books
> > > often to the point of going without food
> > > and that of david c ullrich
> > > with his degrees and professorship
>
> > > i think such a comparison would be highly telling
> > > of his approach to discouraging investigation
> > > which he has shown numerous times on the newsgroups
>
> > Oh, bullshit. Utter, utter bullshit. I also taught myself what little
> > I know about mathematics, and I have received nothing but help from
> > David with my own investigations. Why do you suppose that is? Perhaps
> > it's because I don't post meaningless nonsense and then question
> > people's competence when they aren't able to guess what I would have
> > said if I were able to string a coherent thought together.
>
> can you give an example of meaningless nonsense i have posted?
No. I wasn't referring to you with the above.
> i will try to clear up any questions you may have
>
> > Perhaps
> > it's because I don't post statements which are outright false and then
> > pretend I meant something else when called on it, and then insult
> > people for having disagreed with the statement I never actually wrote.
>
> if i have done this to you
> i apologise right now
You haven't. Sorry if I gave you the wrong impression.
> i would like a reference where i have done this
> so i can learn from my mistakes
>
> > Perhaps it's because, unlike some people, I present evidence of having
> > done enough actual studying on the topics I'm interested in to be able
> > to write stuff about those subjects which isn't complete garbage.
>
> what evidence do i need to provide you?
> photograph?
> results?
See above.
>
> i have posted many results...
> which did you find in error?
>
> > For all the times you've suggested that Tommy should read up on such-
> > and-such in a bid to make sense out of his rantings, do you have any
> > evidence that he's ever actually done so? If he has, it doesn't show.
>
> yes
> i think tommy needs to apply himself more
> and i tell him that
>
> and yes
> i will do so aggressively if i have been aggressed
>
> but still
> tommy has a tendency to raise questions
> that are legitimate and interesting
Sure he does. But that doesn't excuse the behaviours I described
above. Nor does it excuse his habit of pretending to already have
answers for those questions when he clearly doesn't.
> and some
> like ullrich
> are often immediately _and_incorrectly_ hostile
David's hostility towards Tommy is well earned IMO. The number of
times that he has been incorrectly hostile is minuscule compared to
the number of times he has /correctly/ pointed out problems with what
Tommy is saying, only to have Tommy respond with insults (usually
backed up with blatant strawman dishonesty).
> it is that immediacy
> the kind that attacks legitimate mathematics in the process
> that i find offensive
Plenty of legitimate mathematics gets done here with David's help,
rather than his hindrance. Can you not see why Tommy gets treated
differently to, for example, me or Mina_World?
> that is the bullshit
> the utter utter bullshit
>
> > > (and which there are a good deal of past threads
> > > solely about ullrich's uglies)
>
> > Yes, I've seen many threads in which Ullrich is involved in arguments
> > about his conduct. It's also been my judgement in /every single one/
> > of those threads that Ullrich was *right*. Whether he is being accused
> > of incompetence, plagiarism or racism, the charges levelled against
> > him are consistently without merit. Perhaps he suffers fools less
> > gladly that some people, but given how many fools there are around
> > here I don't blame him.
>
> so what is ullrich's point here?
>
> please be clear about it
> since you've attacked me here too
> saying i am unable to be clear
No, I didn't say that.
> do you think it is meaningless to write A^C
> for 2 square matrices A and C of the same size?
I think it's meaningless until somebody offers a definition. It would
have been interesting to see how Tommy would have answered that
question without your help, especially given how he usually answers
such questions.
> you say he is _always_ right
No, I don't.
galathaea
> On Nov 25, 12:31 pm, galathaea <galath...@gmail.com> wrote:
>
> > still sore about my pointing out
> > your own chest-thumping re: predicativism and poincare?
>
> I don't know what you're talking about. Perhaps you have me confused
> with another poster?
no confusion
but it's probably better you didn't see it...
> > can anyone explain ullrich's issue here
> > instead of delighting in the battle?
>
> I may have all kinds of thoughts about Internet conversations, but my
> last post was just, as I thought would be obvious, a bit of fun about
> your seemingly self-serious "I was born in a log cabin and walked six
> miles in the snow to school each day, uphill, both ways"-style plea.
yes
i got the reason for the attack
which i also understood was based on a different poster
(bill)
attacking my substance and capability
i wasn't the one who brought up the comparison
i only offered some facts for the comparison
yes i am defensive
the reasons should be obvious too
MoeBlee
> On Nov 25, 12:47 pm, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > On Nov 25, 12:31 pm, galathaea <galath...@gmail.com> wrote:
>
> > > still sore about my pointing out
> > > your own chest-thumping re: predicativism and poincare?
>
> > I don't know what you're talking about. Perhaps you have me confused
> > with another poster?
>
> no confusion
> but it's probably better you didn't see it...
No, please, you say I was "chest thumping" about predicativism and
Poincare. To what conversation are your referring?
MoeBlee
galathaea
well
if it matters
my call out was in a thread called "punk is dead"
it was concerning a variety of posts
that had happened in a month period
involving just the type of behavior being mentioned here
everyone chest thumps
either defensively or offensively
every now and then
the problem is not the resume
it's the reasons that prompt the resume
the chest thumps
whether from yourself or tommy or someone completely different
don't resolve any mathematical issues
they don't supply proofs where there are none
they simply try to feed a propaganda of authority
and try to play things out
as if they were some type of authority game
that was the whole point in my response to bill
because what i have seen so far in this thread
is an attack of authority
in place of an attack through established meaning
the whole idea of this seems to be
"put tommy in his place"
but if you guys want to put tommy in his place
authority only means the case is already lost
it's an admission of defeat
and tommy knows it
instead
a followup through meaning is much more likely to get somewhere
i've certainly seen tommy's positions evolve
when they have been given a clear demonstration
but when denis or david come in just to mock
it's clear he sees it as the desperation it is
and the deeper problem
the one that tears at me so deeply inside
that i go berserk on usenet almost every time i see it
is that the end result of such posturings
is mostly to just discourage interesting thought
people get embarrassed about asking unusual questions
because they might be seen to be wrong
and therefore
through some strange morbidity
mocked
suffering fools should be the same as suffering children
ignore them if they aren't your own
and you don't want to deal with them
if you want to help them out
then be clear
and teach them where they went wrong
if they are rude to you
then sure
you can be rude back
but don't always expect them to be rude
and preempt them
that's the type of shit that stupid wars get fought over
amy666
> On Mon, 24 Nov 2008 16:30:22 EST, amy666
> <tomm...@hotmail.com>
> wrote:
>
> >David C Ullrich wrote :
> >
> >' bla bla bla nothing about matrix exponentiation or
> matrices that commute ' + ' childish behaviour to
> hide his ignorance '
> >
> >
> >
> >ok david
> >
> >im sick of you telling me to prove myself , while at
> the same time you show the ignorance of e.g. matrix
> exponentiation.
> >
> >you prove yourself this time , since i might have
> actually solved the problem of the OP ,
>
> "might" have. Right.
Right !
and you oh genius math prof david C ullrich HAVE NOT EVEN ATTEMPTED TO ANSWER THE OP AND RESOLVE THE QUESTION !!
typical david !
the professor who insults the attempts of proofs and other math of his students while not giving or even knowing or even trying to give an answer HIMSELF !!
its is OUTRAGIOUS since , assume David gave the answer , he would be the great prof of math on sci.math and i would be nothing ...
but if i give the answer , David is STILL BETTER ???
like suppose id HAD SHOWN IGONORANCE OF MATRIX EXPONENTIATION :
then surely i would be called a crank and david the 'prof'
but now its the other way around , yet same reactions ??????
...
i feel a buzzword coming up , yep got that feeling again ...
...
Never mind the fact that you
> have no evidence
> whatever for the idea that what you posted actually
> gave a solution,
> in fact what you posted is meaningless.
there it is !!
" meaningless "
the buzzword.
if david cant take up a challenge , be sure to expect buzzwords like " meaningless "
what is the difference between JSH insulting others while not knowing matrix exponentiation and writing a book and david insulting others while not knowing matrix exponentiation and writing a book ?
the difference is " meaningless "
i believe " meaningless " is david's favorite word.
perhaps a nice title for his book ( collection of notes rather ! ) :
david's meaninglessness version 1.0
>
> >while you are still trying to figure out
> exponentiation of matrices and log branches.
> >
> >
> >lets turn the tables.
> >
> >you be the student and give me a counterexample to
> >
> >my post made on 19/11/08 in this thread.
> >
> >should be easy for you not ??
apparently you cant " meaningless " david.
>
> That's impossible until you explain what you mean.
> You said
> this:
i mean " meaningless " matrices of the " meaningless " same size.
and ^ means " meaningless " matrix exponentiation.
>
> "
> i believe matrix A and B commute if
>
> - assuming they have abs different from 1 or 0 -
>
> - assuming both are square matrices -
since david never heard of matrix exponentiation he probably doesnt know about square matrices too.
is that the part you dont understand about matrices , apart from ' commute ' and ' matrix exponentiation ' ?
or is a square matrix " meaningless " ?
>
> if A^C = B for some square matrix C
>
> where C satisfies C D = D C for any square matrix D.
>
> - assuming all matrices are of the same size of
> course -"
>
> When I asked what you meant by A^C you didn't reply -
> then you said yes when g said it was exp(C ln(A)).
because your just trying to trick us.
with something ' branchy ' like ln(A) = ln(A) + 2pi i
and im not going to discuss matrix exponentiation with you, if you act so arrogant or if you insist it isnt well defined.
either your loss , ignorance or mistake.
>
> But you haven't said what you mean by ln(A).
I dont even have too !!
i said if C exists with A^C = B.
you are the one involving logaritms , which has nothing to do with my answer , just trying to invalidate my answer without even knowing about exponentiation or being able to give a COUNTEREXAMPLE.
> (That's a separate question from the question of
> proving the existence of ln(A), which isn't hard,
> although you've ignored the question and g has
> refused to do, instead just replying to corrections
> with insults and complaints.) In fact A has many
> different logarithms - which one are you referring
> to?
>
> You also need to clarify what you mean by
>
> "C satisfies C D = D C for any square matrix D";
>
> do you mean that CD = DC for every D or that
> there exists D such that CD = DC.
for crying out loud , you even quote and still cant read , i said " for every " and you ask : do you mean there exists ? , NO I SAID " for every " and i meant " for every " !!!
sigh.
(Hint: If you
> mean the second that says nothing whatever
> about C. If you mean the first that does put
> a severe restriction on C - of course you don't
> know what it actually does say about C or
> you would not have stated the condition in such
> a clumsy way).
read the hints i gave you above ...
>
> >
> >tommy1729
>
> David C. Ullrich
>
> "Understanding Godel isn't about following his formal
> proof.
> That would make a mockery of everything Godel was up
> to."
> (John Jones, "My talk about Godel to the post-grads."
> in sci.logic.)
regards
tommy1729
MoeBlee
> On Nov 25, 1:17 pm, MoeBlee <jazzm...@hotmail.com> wrote:
> > On Nov 25, 12:58 pm, galathaea <galath...@gmail.com> wrote:
>
> > > On Nov 25, 12:47 pm, MoeBlee <jazzm...@hotmail.com> wrote:
>
> > > > On Nov 25, 12:31 pm, galathaea <galath...@gmail.com> wrote:
>
> > > > > still sore about my pointing out
> > > > > your own chest-thumping re: predicativism and poincare?
>
> > > > I don't know what you're talking about. Perhaps you have me confused
> > > > with another poster?
>
> > > no confusion
> > > but it's probably better you didn't see it...
>
> > No, please, you say I was "chest thumping" about predicativism and
> > Poincare. To what conversation are your referring?
>
> well
> if it matters
> my call out was in a thread called "punk is dead"
I just looked at a thread called "punk is dead" in sci.logic. I'm not
in it. You do mention me in connection with predicativism and
Poincare, but you don't say where I ever was "chest thumping" about
predicativism and Poincare. So all you've done is point me to a thread
where you earlier claimed I said something or other about
predicativism and perhaps (or perhaps not) about Poincare. So, if you
claim I was "chest thumping" about predicativism and Poincare, then
I'd like to know what you are referring to.
By the way, your comments about me in that post there are really quite
a hatchet job of misrepresentations of me. I'll respond to them there.
MoeBlee
Gerry Myerson
<64dd49d3-0848-44f8...@h20g2000yqn.googlegroups.com>,
Chip Eastham <hard...@gmail.com> wrote:
> On Nov 25, 5:58 am, "alainvergh...@gmail.com"
> <alainvergh...@gmail.com> wrote:
> > 1)The example of commutation I've given was built from
> > two different polynomials C =p1(A) , B=p2(A) ,
> > noboby explain me the link with simutanously diagonalizable matrices;
>
> If PAP^-1 is diagonal, and C = p(A) is a polynomial
> in A, then PCP^-1 is also diagonal. All polynomials
> in A are simultaneously diagonalizable if A is
> diagonalizable (similar to a diagonal matrix).
Moreover, if A has no repeated eigenvalues and commutes
with B, then B is a polynomial in A.
--
Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)
Chip Eastham
wrote:
> In article
> <64dd49d3-0848-44f8-b540-e1b4b4d81...@h20g2000yqn.googlegroups.com>,
> Chip Eastham <hardm...@gmail.com> wrote:
>
> > On Nov 25, 5:58 am, "alainvergh...@gmail.com"
> > <alainvergh...@gmail.com> wrote:
> > > 1)The example of commutation I've given was built from
> > > two different polynomials C =p1(A) , B=p2(A) ,
> > > noboby explain me the link with simutanously diagonalizable matrices;
>
> > If PAP^-1 is diagonal, and C = p(A) is a polynomial
> > in A, then PCP^-1 is also diagonal. All polynomials
> > in A are simultaneously diagonalizable if A is
> > diagonalizable (similar to a diagonal matrix).
>
> Moreover, if A has no repeated eigenvalues and commutes
> with B, then B is a polynomial in A.
Well, Gerry, that's your interpolation!
grins, chip
Rotwang
>
> > do you think it is meaningless to write A^C
> > for 2 square matrices A and C of the same size?
>
> I think it's meaningless until somebody offers a definition. It would
> have been interesting to see how Tommy would have answered that
> question without your help, especially given how he usually answers
> such questions.
Incidentally, galathaea, I think you should have a look at this
excerpt from a recent post of Tommy's in this thread:
> > But you haven't said what you mean by ln(A).
> I dont even have too !!
> i said if C exists with A^C = B.
> you are the one involving logaritms , which has nothing to do with
> my answer , just trying to invalidate my answer without even knowing
> about exponentiation or being able to give a COUNTEREXAMPLE.
See that? Tommy says that logarithms have nothing to do with his
answer. So when David asked him what he means by A^C, you replied with
> > wouldn't that just be
> exp(C ln(A))?
and Tommy replied with
> yep thats it.
Tommy was in fact lying. Just as I, and presumably David also,
suspected. He still doesn't have a definition of A^C, by the way. If
he did he'd give it, but instead he whines, insults and throws up
smoke - just like he always does. That isn't the behaviour of someone
interested in "investigation", it's the behaviour of someone who wants
to throw out half-baked rubbish and not get called on it. Whatever you
think of David teasing Tommy, it certainly doesn't demonstrate an
"approach to discouraging investigation".
junoexpress
> Yes, I've seen many threads in which Ullrich is involved in arguments
> about his conduct. ... Perhaps he suffers fools less
> gladly that some people, but given how many fools there are around
> here I don't blame him.
Nobody forces him to be here, so why would he choose to "suffer" so?
Let's start at the beginning of your premise/argument, which is to
suggest his conduct is due to his superior intellect (i.e. "suffering
fools"). Yet, I've always found that people who are well-balanced and
have superior intellects however do not characteristically act nasty
(consider Robert Israel, if you will).
Therefore, the nastiness of a smart person is NOT due to his
intellect: it is the result of having issues (i.e. either not being
satisfied with one's life or being insecure).
But, that's probably representative of a fair percentage of the people
on this ng, (maybe those in this thread?) and may explain part of his
being on it, among all these "fools".
M
galathaea
i could have answered that question at the time
but now i have little idea where to start
i can try to find the thread
but i will have to wade through some really long threads
to try to hunt it down
if it helps ring any bells
the quote i had intended on including
but had removed at the last moment because it was overlong
and needed a lot of context
went something like:
(long back and forth)
(eventually you get frustrated and tell them to read a book)
(they come back asking why YOU don't read a book)
you:
i do read books
not just ZFC but nonstandard logics too
i've read on constructivism and predicative theories
and if you had read even a history of logic
you wouldn't be making the silly mistake of (whatever)
...
or something like that
i apologise if any of the vague recollections are incorrect
(i think you may have added an additional layer of tact
but it had something like that level of frustration apparent)
it was a couple of weeks before you had asked
in some other thread
what poincare had to do with early constructivism
you had asked very earnestly
(please be clear that i do not question your desire to learn)
and even in the thread where you were proppin'
you did not claim that you knew the subjects deeply
that is not my point
whether you knew it or not
it was clear that there was a gap in fundamental relationships
- on poincare's predicativism and atomistic constructivism
which belied a missing history being used as bluster
much like what you were attacking this other poster about
i fully admit that you were frustrated
because you felt their bluster had been clearly exposed
and it had been
but you were doing the same
and i thought
maybe if i got angry at you
you might see that you need to calm down a bit
and i laughed at the irony of the if
but i wasn't really angry at you then
so it had to wait until after i saw the other posters
upon which the thread begins
laughing about crankdom and potential infinity
which did piss me off
then i added your incident to the list
so i could fill an entire tirade
my point was still earnestly intended
and i do hope you heed it
my point was that i think you should back down
you aggress too eagerly
what you sometimes attack as bluster
is not
and what you sometimes feel sound of
turns out to be bluster
it's okay when it's defensive
what i did about proppin' my independent study
was defensive bluster at being attacked
i was saying:
i think i'm working hard at proving myself
so i don't think you should pull the authority card
david ullrich is more frequent at the false attacks
and A^C is just one of the recent examples
i'm not attacking him or you for being wrong
i am wrong more than both of you combined
i am just saying:
come on
isn't it time to cool off some?
david is now going off about how i'm wrong
and how i've refused to answer some questions
and what he thinks i'm wrong about
i would love to know better
but now he seems to want existence proofs
or expositions of analytic continuation on normed spaces
and he's refusing to say he was wrong
like the people he is attacking
i think most people realise
A^C is a legitimate concept
and i've been substantially correct about it's form
and how to extend the definition analytically
i know i interrupted some game
and i know how irritating i can be
but there is some really negative bluster going around
and that is something i have a hard time coexisting with
i know i am ultrasensitive
and i get set off really easy
but this behavior fills me with dread
when people tell me i am nothing
i __feel__ i am nothing
i don't think you realise the depths such feelings may reach
because i think you are use to being hard on yourself
i understand being hard on myself
that's why i bluster defensively
i want to feel good about my pursuits
and be in charge of my own self negation
both you and ullrich are intelligent
and should feel good about your capabilities
but you both need to be more careful about what you attack
and you both need to acknowledge more
when overreaching has occurred
if you guys can't acknowledge when wrong
then why would you guys feign indignation
at all the other trollcrankpotters who cannot?
it's an abuse of trust
and trust networks are all-important in logical analysis
> By the way, your comments about me in that post there are really quite
> a hatchet job of misrepresentations of me. I'll respond to them there.
not at all
you are certainly one who has
over and over
complained that others need to read a book
you are one of the prototypes
who sets a bar just over someone's head
yelling at them that they need to study first order logic
or some other foundation
and keeps the bar just under their own
you write of me giving you a hatchet job?
i've seen you tear apart others
even when there were some clear cases
of you being the one over their head
hell
a quick search on mathforum
of the word "study" used by jack markan
gives a huge number of posts
many of which show you behaving in a berating way
you are precisely the ullrich-protege type i was attacking
i am earnestly concerned
that you may one day be the cause
of someone turning away from mathematical pursuits
just as i am of ullrich
and denis
and tonico
and ...
i've seen protests that it doesn't happen much
that the errored attacks aren't frequent at all
and that the vast majority of attacks are well-deserved
but i still see them all too often
and i see you all so unable to do
what you desperately want from those you interact with
to let the bluster down
and apologise
Denis Feldmann
> On Nov 25, 2:54 pm, Rotwang <sg...@hotmail.co.uk> wrote:
>
>> Yes, I've seen many threads in which Ullrich is involved in arguments
>> about his conduct. ... Perhaps he suffers fools less
>> gladly that some people, but given how many fools there are around
>> here I don't blame him.
>
> Nobody forces him to be here, so why would he choose to "suffer" so?
Perhaps because being here has some advantages, besides being bothered
by fools...
>
> Let's start at the beginning of your premise/argument, which is to
> suggest his conduct is due to his superior intellect (i.e. "suffering
> fools"). Yet, I've always found that people who are well-balanced and
> have superior intellects however do not characteristically act nasty
> (consider Robert Israel, if you will).
> Therefore, the nastiness of a smart person is NOT due to his
> intellect: it is the result of having issues (i.e. either not being
> satisfied with one's life or being insecure).
Which implies ("therefore") that you are not smart or have issues too...
Well, the fact that some people (Robert Israel) are smart and always
nice) is only a proof that this is possible, certainly not that every
smart and not nice people must have personality troubles (have you
considered it could be only a local problem, like bad digestion?)
Denis Feldmann
trickster, liar" Is he a Cretean?)
galathaea
r:
> tommy too
you know
i don't come out here to defend tommy
of anyone here
i think i have the biggest grief with him
as he once tried to claim that my results
were already done by someone
and i panicked that i might yet again
have achieved nothing of value
but you know
there is a past
and there is a future
and there is learning
and learnings not possible
in an environment where the punishment for the past
is ongoing
it's all a package deal anyways
i'm not tommy
ullrich has been belittling here to me
and i guess i don't understand
why it's so horribly wrong that tommy is accused of things
that seem to be excused for ullrich
if you guys want to be blatant about tommy's bluff
why not so for ullrich?
Tonico
>
> i am earnestly concerned
> that you may one day be the cause
> of someone turning away from mathematical pursuits
>
> just as i am of ullrich
>
> and denis
>
> and tonico
>
**************************************************************
Let us all hope you have some good bread and cheese for all that whine
you have, gala.
Particularly enlightening was your latest vicious and ferocious
attacks on David, making a rather nauseating counterpoint with that
marvel of logic and good-behaviour called Amy (Tommy).
Way to go!
Regards
Tonio
galathaea
wrote:
> How much do you bet galathea will never answer that (hint : "fabulist,
> trickster, liar" Is he a Cretean?)
thank you denis
you've been a great illustration
you've missed some errors of mine recently
though
so i still don't get that whole "stalker" vibe
it's okay
you can take it easy over the next few days
it's holidays in america
and all that
but if you need me to email you
so you don't miss out in the future
i can do that for you
i got your back
Angus Rodgers
<MTBre...@gmail.com> wrote:
>Therefore, the nastiness of a smart person is NOT due to his
>intellect: it is the result of having issues (i.e. either not being
>satisfied with one's life or being insecure).
>
>But, that's probably representative of a fair percentage of the people
>on this ng, (maybe those in this thread?) and may explain part of his
>being on it, among all these "fools".
I refuse to belong to a newsgroup that would have me as a
member!
--
Angus Rodgers
David C. Ullrich
<gala...@gmail.com> wrote:
>On Nov 25, 12:18 pm, galathaea <galath...@gmail.com> wrote:
>
>> please be clear about it
>> since you've attacked me here too
>> saying i am unable to be clear
>
>i am most interested in this part
>
>be as clear as absolutely possible
> in explaining what this is all about
>
>i didn't attack you
>
>so far
> several have jumped in to attack me
>but no one has explained how it was proper
>for ullrich to demean the idea of matrix exponentiation
> and follow with several posts claiming i am wrong about something
> without illustrating any errors
You stated that ln(A) can be defined by a power series.
That's simply not true.
(Not true in general - of course it's true for _some_ A,
but not for all A with determinant not equal to 0 or 1).
>do you see how people like jsh
> could get erroneous ideas about mathematicians?
>
>you say ullrich doesn't suffer fools kindly
>
>i don't like being a fool
> it isn't something that i desire flaunting in front of everyone
>
>a simple explanation seems like it might be worthwhile
>
>i mean
> you guys do that for james when he is really far gone
>so if you'd just do it for me
> maybe i could learn and stuff...
>
>-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
>galathaea: prankster, fablist, magician, liar
David C. Ullrich
David C. Ullrich
wrote:
>david wrote :
>
>> On Mon, 24 Nov 2008 16:30:22 EST, amy666
>> <tomm...@hotmail.com>
>> wrote:
>>
>> >David C Ullrich wrote :
>> >
>> >' bla bla bla nothing about matrix exponentiation or
>> matrices that commute ' + ' childish behaviour to
>> hide his ignorance '
>> >
>> >
>> >
>> >ok david
>> >
>> >im sick of you telling me to prove myself , while at
>> the same time you show the ignorance of e.g. matrix
>> exponentiation.
>> >
>> >you prove yourself this time , since i might have
>> actually solved the problem of the OP ,
>>
>> "might" have. Right.
>
>
>Right !
>
>and you oh genius math prof david C ullrich HAVE NOT EVEN ATTEMPTED TO ANSWER THE OP AND RESOLVE THE QUESTION !!
I don't know whether you noticed, but there have been many replies
in this thread, talking about things like eigenspaces,
diagonalizability, etc, that actually _do_ say something
useful about the question.
>typical david !
>
>the professor who insults the attempts of proofs and other math of his students while not giving or even knowing or even trying to give an answer HIMSELF !!
>
>
>its is OUTRAGIOUS since , assume David gave the answer , he would be the great prof of math on sci.math and i would be nothing ...
>
>but if i give the answer , David is STILL BETTER ???
>
>
>like suppose id HAD SHOWN IGONORANCE OF MATRIX EXPONENTIATION :
>
>then surely i would be called a crank and david the 'prof'
>
>but now its the other way around , yet same reactions ??????
>
>
>...
>
>i feel a buzzword coming up , yep got that feeling again ...
>
>...
>
>
>
>
>
> Never mind the fact that you
>> have no evidence
>> whatever for the idea that what you posted actually
>> gave a solution,
>> in fact what you posted is meaningless.
>
>
>there it is !!
>
>" meaningless "
>
>the buzzword.
>
>if david cant take up a challenge , be sure to expect buzzwords like " meaningless "
Sorry, Timmy, but it's not going to work. It's clear to everyone
that you simply haven't explained what you meant - complaining
about my use of the word "meaningless" doesn't change that.
Guffaw. A matrix _does_ have more than one log - if
you give a "definition" involving ln(A) that _is_
meaningless until you specify _which_ ln(A) you
have in mind.
So I'm trying to trick you, by simply asking you to
explain what you meant?
>and im not going to discuss matrix exponentiation with you, if you act so arrogant or if you insist it isnt well defined.
>
>either your loss , ignorance or mistake.
>
>
>>
>> But you haven't said what you mean by ln(A).
>
>I dont even have too !!
>
>i said if C exists with A^C = B.
>
>you are the one involving logaritms , which has nothing to do with my answer , just trying to invalidate my answer without even knowing about exponentiation or being able to give a COUNTEREXAMPLE.
Huh? At the start of all this I asked what you meant by A^C.
You didn't reply. g said it was exp(C ln(A)). You said
yes, that's it.
If the definition _is_ exp(C ln(A)) then you _do_ need to
specify which ln(A) you mean, or you haven't defined
anything. The "branchiness" of ln is the way things
are, not something that was invented to trick you.
_Now_ you say that ln(A) has nothing to do with the
definition of A^C? This raises two questions:
(i) Then why did you agree that the definition _was_ exp(C ln(A))?
(ii) Ok, then what _is_ the definition of A^C you had in mind?
>
>
>> (That's a separate question from the question of
>> proving the existence of ln(A), which isn't hard,
>> although you've ignored the question and g has
>> refused to do, instead just replying to corrections
>> with insults and complaints.) In fact A has many
>> different logarithms - which one are you referring
>> to?
>>
>> You also need to clarify what you mean by
>>
>> "C satisfies C D = D C for any square matrix D";
>>
>> do you mean that CD = DC for every D or that
>> there exists D such that CD = DC.
>
>for crying out loud , you even quote and still cant read , i said " for every " and you ask : do you mean there exists ? , NO I SAID " for every " and i meant " for every " !!!
No, you didn't say "for every", you said "any", which is ambiguous.
So you meant "for every D", great. You're complaining about my
inability to read your mind, trying to make it into my ignorance
instead. You obviously don't know _which_ matrices
C have the property that CD = DC for every D, because
if you did you would have stated the condition much more
simply.
Oops. Of course you do know that. So tell us: CD = DC for every D
if and only if C satisfies _what_ very simple condition?
Marko Amnell
> On Tue, 25 Nov 2008 18:33:07 -0800 (PST), junoexpress
>
> >Therefore, the nastiness of a smart person is NOT due to his
> >intellect: it is the result of having issues (i.e. either not being
> >satisfied with one's life or being insecure).
>
> >But, that's probably representative of a fair percentage of the people
> >on this ng, (maybe those in this thread?) and may explain part of his
> >being on it, among all these "fools".
>
> I refuse to belong to a newsgroup that would have me as a
> member!
Better a newsgroup that discusses
Perelman than Marx.
Angus Rodgers
<gala...@gmail.com> wrote:
>i know i am ultrasensitive
> and i get set off really easy
>but this behavior fills me with dread
>
>when people tell me i am nothing
>i __feel__ i am nothing
>
> i don't think you realise the depths such feelings may reach
> because i think you are use to being hard on yourself
>
>i understand being hard on myself
>
>that's why i bluster defensively
>
>i want to feel good about my pursuits
>and be in charge of my own self negation
Perhaps I may: (a) read your phrase "self negation" as "reason"
(and/or "ethics" and/or "morality", but it is reason that I want
to focus on); and (b) go off on a self-analytical tangent (which
I'll try to excuse as an effort to extract some general issues
out of this struggle of David versus Goliathaea). :-)
I've been struggling to understand something very painful about
myself for about 37 years now. I think what has been most fatal
to me has been a deeply ingrained (and silent, non-hallucinatory)
"voice" which tells me, most compellingly, that my reason is not
capable of addressing anything in the human world (that is real).
(There are many other such silent, non-hallucinatory "voices",
but there is good reason to single this one out for attention.)
It is as if I am made of the wrong stuff for this world, or am
from another planet, and, if I am to function here at all, can
only do so by pretending to be human, feeling all the time like
a spy in enemy territory, unable to go home, forced to live his
cover story as if it were real, to the extent that any other
reality is forgotten. A sleeper. (But this is getting ahead of
my story, such as it is.)
For a few brief (and already insecure) years in my youth, I managed
to counter this silent "voice" with another silent "voice" of my
own, which told me (also quite compellingly) that, although totally
unable to function in the "real world" ... (I dared not and could
not argue with the other "voice" that told me so. After all, I had
been brought up to think that way about myself. The silent "voice"
in my head had originally been another very loud and angry voice,
in the "real world", backed up by an uncontested power of physical
and verbal punishment, unopposed by any other voice in the "real
world".) ... I had a special ability to function in another place.
I could do mathematics, or at least pure mathematics, just so long
as I did not think of it as existing in the "real world". (Fatally,
this meant that I could not talk to anyone about it, not even when
I got to university.)
At university I had to realise that mathematics and mathematicians
existed in the "real world". (A whole lot else went on as well -
but again, I'm trying to focus on one issue that now seems to me
to have been decisive.) I collapsed almost completely, and I have
been in a state of collapse ever since. I function better the less
I have to do with other people in the "real world". The Internet
suits me well, but I find even it hard to cope with. I've had to
withdraw from sci.math a few times, over the years. It continues
to represent a kind of compromise, hybrid place to me, where I am
not free to float around in a world of my own, but nor am I bound
in slavery. I am not in charge, but nor is anyone (or anything)
completely in charge of me.
With great difficulty (the problems are numerous and horrendous,
even though, by the standards of most human beings throughout
history and across the world, I live a comfortable and even
privileged existence), I am slowly re-learning that my reason is
able to address mathematics (pure, and even perhaps also applied),
and (perhaps as a result of the long and complicated struggle I
have had to achieve even the little that I have) also that it is
not limited to mathematics. (This is also because mathematics is
part of the "real world", therefore, if I can address mathematics,
it cannot be true that I cannot reason about anything in the "real
world", i.e. the "voice" has been lying to me all these years).
In a word, I am slowly recovering my reason.
I "realise the depths such feelings may reach". (Perhaps some
others here do, too - and even those that don't understand may
be involved in some of the same issues.) That's what I'm saying.
I could (obviously) go on much longer about this, but that's
probably more than long enough for a post to sci.math! I'm
sorry if it was completely and utterly irrelevant.
--
Angus Rodgers
MoeBlee
> (eventually you get frustrated and tell them to read a book)
> (they come back asking why YOU don't read a book)
> you:
> i do read books
> not just ZFC but nonstandard logics too
> i've read on constructivism and predicative theories
> and if you had read even a history of logic
> you wouldn't be making the silly mistake of (whatever)
Neither that paraphrase nor anything you've posted even SUGGESTS that
there is an example of me "chest thumping" about predicativism and
Poincare.
(1) I've never claimed to be an expert on the subjects of non-standard
logics, constructivism, predicativism, Poincare, or even classical set
theory, mathematical logic, or mathematics. I am well versed in
certain BASICS of the subject of mathematical logic and set theory,
but rather than "chest thump" about such special subjects as
predicativism and Poincare, I've been pretty humble to admit that I
have much more to learn, as I even have much more to learn even about
classical mathematical logic, set theory, and mathematics.
So your characterization of "chest thumping" about predicativism and
Poincare is completely unjustified.
(2) When I tell a person to read a textbook on the subject, it is when
the person is either spouting incorrectly about the subject or is
asking questions that need to be informed by a more systematic
understanding as is gained by reading a textbook.
(3) I am not generally intolerant simply for a person making a
mistake, but rather I am irked by people who continue to REPEAT basic
mistakes while refusing to learn the basics of the subject.
> it was a couple of weeks before you had asked
> in some other thread
> what poincare had to do with early constructivism
Though it is possible I did ask that specific question, I don't recall
asking it. I have known for a long time that Poincare is associated
with constructivism and I know something about that, though not in
great detail. Perhaps I was asking about some specific point.
> you had asked very earnestly
> (please be clear that i do not question your desire to learn)
> and even in the thread where you were proppin'
> you did not claim that you knew the subjects deeply
So, that's not "chest thumping" about predicativism and Poincare! And
now you add that I was "proppin'" about something or other, again
unsubstantiated.
> that is not my point
>
> whether you knew it or not
> it was clear that there was a gap in fundamental relationships
> - on poincare's predicativism and atomistic constructivism
> which belied a missing history being used as bluster
> much like what you were attacking this other poster about
What the HELL kind of twisted logic is that? I didn't "bluster" based
on something I didn't know about.
> i fully admit that you were frustrated
> because you felt their bluster had been clearly exposed
>
> and it had been
>
> but you were doing the same
It's becomming pretty clear to me that your dislike of my posting
style is causing you to quite twist my comments and the conversational
events. You STILL have not shown that I "chest thumped" about
predicativism and Poincare (indeed YOU even admit that I was sincerely
ASKING about the subject), yet NOW you go on to make ADDITIONAL
UNSUBSTANTIATED and VAGUE claims that I was "blustering" about
something or other.
> you aggress too eagerly
That is a matter of judgement. I don't deny that I am often harsh.
Whether my harsheness is too often unjustified or too frequent is a
judgement you have the prerogative to make. But it is a separate
matter from whether I have "chest thumped" or "blustered" on some
subject such as predicativism or Poincare.
> i don't think you should pull the authority card
I DON'T. I do NOT claim that my assertions deserve special
consideration by my being an authority, since I don't even claim to be
an authority. I do have a good grasp of certain basics, and all I
"pull" in that regard is that I GIVE actual arguments (at least until
the poster has exhausted my patience) using those basics, and only
when, as far as I can tell, the matter at hand is resolved by said
basics and not by some more advanced material with which I am not
fluent.
> you are certainly one who has
> over and over
> complained that others need to read a book
WHEN the person is repeating basic mistakes, especially arrogantly and
dogmatically so, or is asking about stuff that needs first to be
informed by prior material.
> you are one of the prototypes
> who sets a bar just over someone's head
> yelling at them that they need to study first order logic
> or some other foundation
> and keeps the bar just under their own
No, I do NOT tendentiously spout about material that I haven't got a
solid grasp on. The "bar" is ALWAYS higher than me. I am in constant
recognition that what I know is miniscule.
What you wrote in the other thread about me IS a hatchet job, and
you're only making it worse here.
Like you, I too have some serious thoughts about posting and what goes
on in forums (I didn't include here some or your quotes on that
general subject, since a few of them I don't disagree with and also
first I need to fend your incorrect claims about me, and also because
in other forums I've pretty much exhausted myself on the subject). But
on certain forum matters I do have a basically different view from
yours. And I very much don't appreciate your hatchet-job
mischaracterizations of what I have posted and the manner in which
I've posted it.
MoeBlee
lwa...@lausd.net
> On Tue, 25 Nov 2008 16:52:30 EST, amy666 <tommy1...@hotmail.com>
> wrote:
> >there it is !!
> >" meaningless "
> >the buzzword.
> >if david cant take up a challenge , be sure to expect buzzwords like " meaningless "
> Sorry, Timmy, but it's not going to work. It's clear to everyone
> that you simply haven't explained what you meant - complaining
> about my use of the word "meaningless" doesn't change that.
OK, I just discovered this thread and saw how quickly it
was growing, so I decided to check it out to see what's
going on here.
Most long threads here at sci.math are debates about ZFC
and standard analysis -- specifically over whether there
can be new set theories in which the negations of some
theorem of ZFC (usually Cantor's theorem) is provable,
and whether such theories are inconsistent.
But this thread deals with standard ZFC and standard
reals -- more specifically, with matrices whose entries
are standard real (or complex) numbers. Yet we see a
similar debate (and similar factions) regarding whether
something can be defined in standard linear algebra.
It all began when tommy1729 sought a definition of
matrix exponentiation. Once again, I can probably figure
out why -- once we can find A^C (A,C matrices), we can
find A^A and thus we can define matrix tetration, and
we already know that tommy1729 is a tetration fan.
When Dr. Ullrich asked tommy1729 to define matrix
exponentiation, galathaea responded by attempting to
define exponentiation in terms of a logarithm, just as
standard exponentiation of reals (or complexes) can be
defined in terms of the standard logarithm. And this
started a huge debate over whether there can be a matrix
logarithm in linear algebra.
The reason that he isn't being more helpful is that he
most likely _wants_ galathaea and tommy1729 to fail. Yes,
like many standard mathematicians, Ullrich doesn't _want_
sci.math posters to define anything new, whether it's a
new set theory or a new concept within standard theory
such as matrix exponentiation.
That's the reason that Ullrich, and many standard
mathematicians, use what tommy1729 calls "buzzwords"
such as "meaningless," "useful," etc., to describe
novel concepts set theories.
> >because your just trying to trick us.
> >with something ' branchy ' like ln(A) = ln(A) + 2pi i
> Guffaw. A matrix _does_ have more than one log - if
> you give a "definition" involving ln(A) that _is_
> meaningless until you specify _which_ ln(A) you
> have in mind.
I disagree. We define complex exponentiation z^t:
z^t = exp(t log(z)).
without declaring which logarithm we want. Then exponentiation
is multivalued, just as log itself is. How many values does
z^t have? For nonzero z:
q, if teQ and t=p/q, q>0 lowest terms
aleph_0 otherwise
So why can't we have matrix exponentiation to be
as multivalued as log?
Then again, maybe there is a way to specify a
particular logarithm.
I tried typing "principal matrix logarithm" into a
search engine. I _know_ that any result that the
search engine might returned will not be a textbook,
but as I've posted numerous times, not everyone has
access to a book in which matrix logarithm is defined.
The first result turned out to be a MATLAB page which
defines the principal matrix logarithm as the one
whose eigenvalues have imaginary part between -n and n,
though the site failes to define "n." (Maybe it's the
size of the matrix, nxn? I can't tell!) Still, we can
see that a principal logarithm can defined as the one
whose eigenvalues have imaginary part with as small an
absolute value as possible. The site also states that
if one of the eigenvalues is on the negative real
axis, then there is no principal logarithm, and if one
of the eigenvalues is zero, then there's no log at all
(MATLAB returns infinity).
It might have been helpful if Ullrich explained how
principal values of the logarithm works, but again, he
doesn't because he _wants_ tommy1729 to fail to
define a new matrix operation.
> Huh? At the start of all this I asked what you meant by A^C.
> You didn't reply. g said it was exp(C ln(A)). You said
> yes, that's it.
> If the definition _is_ exp(C ln(A)) then you _do_ need to
> specify which ln(A) you mean, or you haven't defined
> anything.
No, we don't. We can let A^C be multivalued, just as we let
z^t (complex z,t) be multivalued. If Ullrich insists that we
choose a value, then fine, choose the _principal_ value, when
it exists.
Of course, I assume that we'll lose (A^C)(A^D) = A^(C+D), just
as we do for complex numbers -- (z^t)(z^u) isn't always equal
to z^(t+u), if we only use principal values. It may be interesting
to see what happens in special cases, such as if all the
eigenvalues are real and positive (just as (x^m)(x^n)=x^(m+n)
works when all the variables are real and positive).
> >> You also need to clarify what you mean by
> >> "C satisfies C D = D C for any square matrix D";
> So you meant "for every D", great. You're complaining about my
> inability to read your mind, trying to make it into my ignorance
> instead. You obviously don't know _which_ matrices
> C have the property that CD = DC for every D, because
> if you did you would have stated the condition much more
> simply.
> Oops. Of course you do know that. So tell us: CD = DC for every D
> if and only if C satisfies _what_ very simple condition?
It would have been simple enough for Ullrich, who
obviously knows the correct answer, just simply
to write what that condition is.
If I had to guess, I'd say the simple condition is
that C must be either the zero matrix, the
identity matrix, or the product of a scalar and
the identity matrix. Obviously, this condition is
sufficient, but I can't find a source (text or
online) that states this. Most sources define
commutativity in general, but most don't state a
general case for when two matrices commute (which
is why this thread exists in the first place). If
a book does mention this, it's more likely to leave
it as an exercise than state it outright.
I've taken a course in linear algebra. But it was
never stated explicity that CD = DC for every D
if and only if C = lambda I for some lambda (or
whatever the correct condition is, if I'm wrong).
So if even I can't find a source that states
directly and explicitly that CD = DC for every D
if and only if C = lambda I for some lambda (or
whatever the correct condition is, if I'm wrong),
then why should we expect tommy1729 to know it?
But if Ullrich knows the correct condition, then it
would be helpful if he stated it. But again, he
doesn't because he _wants_ tommy1729 to fail to
define a new matrix operation.
If someone claims to have proved Goldbach, Riemann, etc.,
using elementary math, I can understand why a sci.math
poster being unhelpful, but not when someone is trying
to invent something new.
Also, I can understand someone not being helpful when
someone just posts homework problems and expects quick,
easy answers. But it's clear that this isn't a homework
problem at all -- since tommy1729 isn't even the OP of
this thread!
I'm _glad_ that Dr. Ullrich isn't my teacher. A good
teacher doesn't belittle students who are trying to
learn, the same way that Ullrich belittles tommy1729,
galathaea, and others. One doesn't inspire people to
learn by saying that their ideas are "meaningless" or
outright lies.
And so I end my post, reiterating the definition:
A^C = exp(C log A)
where both A^C and log(A) are multivalued, whenever
the log is defined. And if we want a principal value
for A^C, then we can take the principal value of the
log, whenever a principal value is defined.
And if tommy1729 wants to define tetration, then I'd
suggest taking the principal value.
lwa...@lausd.net
> On Nov 25, 10:06 pm, galathaea <galath...@gmail.com> wrote:
> > (eventually you get frustrated and tell them to read a book)
> > (they come back asking why YOU don't read a book)
> > you:
> > i do read books
> > not just ZFC but nonstandard logics too
> > i've read on constructivism and predicative theories
> > and if you had read even a history of logic
> > you wouldn't be making the silly mistake of (whatever)
> the person is either spouting incorrectly about the subject or is
> asking questions that need to be informed by a more systematic
> understanding as is gained by reading a textbook.
Just as in the set theory threads, here we have yet another
debate about reading textbooks.
Once again, I point out that not everyone has access to the
textbooks that MoeBlee does.
> (3) I am not generally intolerant simply for a person making a
> mistake, but rather I am irked by people who continue to REPEAT basic
> mistakes while refusing to learn the basics of the subject.
If by "refusing to learn," MoeBlee means "refusing to
read a textbook," then there may be many reasons that
one may refuse to read a textbook, including access
to the proper textbook.
I've been accused of refusing to learn several times on
sci.math (especially lately by Feldmann). The reality is
that I'm actually very _eager_ to learn. I just refuse to
buy a textbook that I can't afford.
Jesse F. Hughes
> The reason that he isn't being more helpful is that he most likely
> _wants_ galathaea and tommy1729 to fail. Yes, like many standard
> mathematicians, Ullrich doesn't _want_ sci.math posters to define
> anything new, whether it's a new set theory or a new concept within
> standard theory such as matrix exponentiation.
Well, you found him out. Whatever did the oppressed do before you
came along?
Stayed oppressed, I'd wager. No more!
Perhaps Ullrich has nothing against new mathematical ideas, whether
found on Usenet or elsewhere. Perhaps he has some other reason for
responding as he does. But it's a lot more fun to guess about
nefarious motives, ain't it?
--
"Now I realize that he got away with all of that because sci.math is
not important, and the rest of the world doesn't pay attention.
Like, no one is worried about football players reading sci.math
postings!" -- James S. Harris on jock reading habits
** Posted from http://www.teranews.com **