solving: inv(A+B)
Zdislav V. Kovarik
Brett George <b.ge...@clarityeq.com> wrote:
:Is there a method (or identity) in which you could solve the matrix
:problem inv(A+B), in terms of A,B,inv(A) and inv(B)?
:
:I need this because inv(A) and inv(B) are easy to solve, while there sum
:is not.
:
:Thanks in advance.
:
:Brett
:
Remark number 0: Do you really, vitally need the inverse? Won't a
factorization be equally satisfactory? (Or even more satisfactory, if the
special structure allows it?)
(Factorizations: permutation*lower triangular*upper triangular, or
orthogonal*upper triangular, or several others)
Remark number 2: You will need more information, or more structure, and
more specific description of what you are willing to invest and what you
want to avoid.
Even with numbers, how do you express 1/(e + pi) using e, pi, 1/e, 1/pi,
additions, multiplications, but no more divisions? (That is, if that's
what you had in mind when asking about matrices.) I don't have a proof
that you can't, but you would surprise many by finding out that you can.
Some answers are available, given more info: inverse of a matrix modified
by adding a low-rank matrix, or approximate inverse of a matrix perturbed
by a small addition, update of a factorization after such modifications,
update of factorization after additive modification by a multiple of
identity, and others. Consult "Matrix Computations" by Golub and Van Loan,
and inspect a publicly available collection of software, such as LAPACK.
Good luck, ZVK(Slavek).
Julius Kusuma
try the matrix inversion lemma! go to any search engine and search for it!
On Sat, 18 Mar 2000, Brett George wrote:
> Is there a method (or identity) in which you could solve the matrix problem
> inv(A+B), in terms of A,B,inv(A) and inv(B)?
>
> I need this because inv(A) and inv(B) are easy to solve, while there sum is
> not.
>
> Thanks in advance.
>
> Brett
>
>
>
>
--
BASiCS Group, University of California at Berkeley
Berkeley Audio-visual Signal Processing and Communication Systems
http://www.eecs.berkeley.edu/~kusuma
opinion of author does not necessarily reflect the opinion of parties
affiliated
I'll procrastinate tomorrow....
-- Jim Davis
Virgil
>Is there a method (or identity) in which you could solve the matrix problem
>inv(A+B), in terms of A,B,inv(A) and inv(B)?
>
>I need this because inv(A) and inv(B) are easy to solve, while there sum is
>not.
>
>Thanks in advance.
>
>Brett
>
>
The existence of inv(A) and inv(B) is no guarantee that there will be a
matrix inv(A+B).
Even if inv(A+B) exists, there is no general way to express it in terms
of A,B,inv(A) and inv(B).
--
Virgil
vm...@frii.com
Brett George
Clay S. Turner
"Zdislav V. Kovarik" wrote:
other stuff snipped
> Even with numbers, how do you express 1/(e + pi) using e, pi, 1/e, 1/pi,
> additions, multiplications, but no more divisions? (That is, if that's
> what you had in mind when asking about matrices.) I don't have a proof
> that you can't, but you would surprise many by finding out that you can.
Well it is not very computationally efficient but here goes
1/(e+pi) = (1/pi)(1-(e/pi)+(e/pi)^2-(e/pi)^3+(e/pi)^4+...) = appr .1707
and (e/pi) is just e times 1/pi, so we have a solution in terms of two
of the four quantities you gave and the three "easy" arithmetic
operations.
Clay
>
> Good luck, ZVK(Slavek).
Pertti Lounesto
> "Brett George" <b.ge...@clarityeq.com> wrote:
>
> >Is there a method (or identity) in which you could solve the matrix problem
> >inv(A+B), in terms of A,B,inv(A) and inv(B)?
> >
> >I need this because inv(A) and inv(B) are easy to solve, while there sum is
> >not.
>
> The existence of inv(A) and inv(B) is no guarantee that there will be a
> matrix inv(A+B).
>
> Even if inv(A+B) exists, there is no general way to express it in terms
> of A,B,inv(A) and inv(B).
Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
Rob Johnson
kov...@mcmail.cis.McMaster.CA (Zdislav V. Kovarik) wrote:
>In article <9533435...@mel.ihug.com.au>,
>Brett George <b.ge...@clarityeq.com> wrote:
>:Is there a method (or identity) in which you could solve the matrix
>:problem inv(A+B), in terms of A,B,inv(A) and inv(B)?
>:
>:I need this because inv(A) and inv(B) are easy to solve, while there sum
>:is not.
> Even with numbers, how do you express 1/(e + pi) using e, pi, 1/e, 1/pi,
>additions, multiplications, but no more divisions? (That is, if that's
>what you had in mind when asking about matrices.) I don't have a proof
>that you can't, but you would surprise many by finding out that you can.
For numbers you can always find one that is smaller than the other and
use the expansion of 1/(1+x) for |x| < 1:
1 1 1
------ = -- ----------
e + pi pi 1 + (e/pi)
1 2 3
= -- ( 1 - (e/pi) + (e/pi) - (e/pi) + ... )
pi
where e/pi = e(1/pi).
However, this doesn't work for matrices. Even if det(A) != det(B) so
that we can find one of A inv(B) or B inv(A) whose determinant is less
than 1, it is not assured that M^n will tend to 0 just because its
determinant does; for example, [[2 0][0 1/3]].
In argument against such a method, I would suggest considering
A = [[1 0][0 1]] and B = [[0 1][1 0]]. Both are invertible, in fact
each is its own inverse. However, inv(A+B) does not exist. This rules
out most simple formulas involving A, B, inv(A), and inv(B).
Rob Johnson
robj...@idt.net
Johannes H Andersen
Brett George wrote:
>
> Is there a method (or identity) in which you could solve the matrix problem
> inv(A+B), in terms of A,B,inv(A) and inv(B)?
>
> I need this because inv(A) and inv(B) are easy to solve, while there sum is
> not.
>
If B = UV, then there is the Sherman-Morrisson-Woodbury formula:
(A+B)^-1 = A^-1 - A^-1U(I + VA^-1U)^-1VA^-1 .
This may be an advantage if U and V' are of size m x n and n << m . It is the
generalisation of the rank-1 update.
Johannes
David C. Ullrich
centuries old. This explains why you would know nothing about
it. If I were you I'd be _proud_ of knowing nothing about the
notion of convergence. But you need to be aware that not
everyone will see it that way: When you (i) continually castigate
others for their ignorance and then (ii) make posts like this,
"correcting" others, and showing that you think that every
infinite series converges, people are going to think that you
never took a calculus course.
I mean of course you never took calculus, that's mathematics
from the previous millenium. But there are several posts here
already giving correct versions of an infinite-series "solution".
They're posts that were posted in this millenium; you should
study them.
Pertti Lounesto wrote:
> Virgil wrote:
>
> > "Brett George" <b.ge...@clarityeq.com> wrote:
> >
> > >Is there a method (or identity) in which you could solve the matrix problem
> > >inv(A+B), in terms of A,B,inv(A) and inv(B)?
> > >
> > >I need this because inv(A) and inv(B) are easy to solve, while there sum is
> > >not.
> >
Randy Yates
>
> Virgil wrote:
>
> > "Brett George" <b.ge...@clarityeq.com> wrote:
> >
> > >Is there a method (or identity) in which you could solve the matrix problem
> > >inv(A+B), in terms of A,B,inv(A) and inv(B)?
> > >
> > >I need this because inv(A) and inv(B) are easy to solve, while there sum is
> > >not.
> >
> > The existence of inv(A) and inv(B) is no guarantee that there will be a
> > matrix inv(A+B).
> >
> > Even if inv(A+B) exists, there is no general way to express it in terms
> > of A,B,inv(A) and inv(B).
>
> Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
Wrong (in general). Let A=0 and B=1.
--
% Randy Yates % "Remember the good old 1980's, when
%% DIGITAL SOUND LABS % things were so uncomplicated?"
%%% Digital Audio Sig. Proc. % 'Ticket To The Moon'
%%%% <ya...@ieee.org> % *Time*, Electric Light Orchestra
http://207.87.184.178/index.htm
Johannes H Andersen
Pertti Lounesto wrote:
>
> Virgil wrote:
>
> > "Brett George" <b.ge...@clarityeq.com> wrote:
> >
> > >Is there a method (or identity) in which you could solve the matrix problem
> > >inv(A+B), in terms of A,B,inv(A) and inv(B)?
> > >
> > >I need this because inv(A) and inv(B) are easy to solve, while there sum is
> > >not.
> >
> > The existence of inv(A) and inv(B) is no guarantee that there will be a
> > matrix inv(A+B).
> >
> > Even if inv(A+B) exists, there is no general way to express it in terms
> > of A,B,inv(A) and inv(B).
>
> Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
Do you mean:
inv(A+B) = inv(A)+inv(A)(-B) inv(A)+inv(A)(-B) inv(A) (-B) inv(A)+...
Converges if the spectral radius of inv(A)B is less than 1. Otherwise ?
Johannes
Johannes H Andersen
Pertti Lounesto wrote:
>
> Virgil wrote:
>
> > "Brett George" <b.ge...@clarityeq.com> wrote:
> >
> > >Is there a method (or identity) in which you could solve the matrix problem
> > >inv(A+B), in terms of A,B,inv(A) and inv(B)?
> > >
> > >I need this because inv(A) and inv(B) are easy to solve, while there sum is
> > >not.
> >
> > The existence of inv(A) and inv(B) is no guarantee that there will be a
> > matrix inv(A+B).
> >
> > Even if inv(A+B) exists, there is no general way to express it in terms
> > of A,B,inv(A) and inv(B).
>
> Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
Converges if the spectral radius of inv(A)B is less than 1. Otherwise ?
Johannes
Joe Skrap
Without making any promises, I think that one of these "special"
instances is when A and B commute, ie when AB=BA.
It would therefore be helpful to know exactly what A and B look like.
By the way, do you actually need find inv(A+B), or just solve
(A+B)x=b?
/K
Dik T. Winter
> > Even if inv(A+B) exists, there is no general way to express it in terms
> > of A,B,inv(A) and inv(B).
>
> Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
Lessee. A = [ 1 0 ] B = [ 1 0 ]
[ -1 1 ] [ 1 1 ]
inv( 1 0 ) = [ 1 0 ] + [ 1 0 ] + [ 1 0 ] + [ 1 0 ] + [ 1 0 ] + ...
( 0 1 ) [ 1 1 ] [ 3 1 ] [ 5 1 ] [ 7 1 ] [ 9 1 ]
Does not look quite right.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
Doug Norris
>In article <38D32BE7...@hit.fi> Pertti Lounesto <Pertti....@hit.fi> writes:
> > > Even if inv(A+B) exists, there is no general way to express it in terms
> > > of A,B,inv(A) and inv(B).
> >
> > Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
>Lessee. A = [ 1 0 ] B = [ 1 0 ]
> [ -1 1 ] [ 1 1 ]
>inv( 1 0 ) = [ 1 0 ] + [ 1 0 ] + [ 1 0 ] + [ 1 0 ] + [ 1 0 ] + ...
> ( 0 1 ) [ 1 1 ] [ 3 1 ] [ 5 1 ] [ 7 1 ] [ 9 1 ]
>Does not look quite right.
Look at that, Pertti! People are disproving your mathematics, just like you
wanted. Good work.
Now we can disrespect you as a mathematician, not just as a person.
Doug
Johannes H Andersen
Randy Yates wrote:
>
> Pertti Lounesto wrote:
> >
> > Virgil wrote:
> >
> > > "Brett George" <b.ge...@clarityeq.com> wrote:
> > >
> > > >Is there a method (or identity) in which you could solve the matrix problem
> > > >inv(A+B), in terms of A,B,inv(A) and inv(B)?
> > > >
> > > >I need this because inv(A) and inv(B) are easy to solve, while there sum is
> > > >not.
> > >
> > > The existence of inv(A) and inv(B) is no guarantee that there will be a
> > > matrix inv(A+B).
> > >
> > > Even if inv(A+B) exists, there is no general way to express it in terms
> > > of A,B,inv(A) and inv(B).
> >
> > Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
>
> Wrong (in general). Let A=0 and B=1.
Not a valid counterexample. inv(A) must exist.
Johannes
Pertti Lounesto
> "Dik T. Winter" <Dik.W...@cwi.nl> writes:
>
> >In article <38D32BE7...@hit.fi> Pertti Lounesto <Pertti....@hit.fi> writes:
> > > > Even if inv(A+B) exists, there is no general way to express it in terms
> > > > of A,B,inv(A) and inv(B).
> > >
> > > Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
>
> >Lessee. A = [ 1 0 ] B = [ 1 0 ]
> > [ -1 1 ] [ 1 1 ]
>
> >inv( 1 0 ) = [ 1 0 ] + [ 1 0 ] + [ 1 0 ] + [ 1 0 ] + [ 1 0 ] + ...
> > ( 0 1 ) [ 1 1 ] [ 3 1 ] [ 5 1 ] [ 7 1 ] [ 9 1 ]
>
> >Does not look quite right.
>
> Look at that, Pertti! People are disproving your mathematics, just like you
> wanted. Good work.
>
> Now we can disrespect you as a mathematician, not just as a person.
Exactly. And you came here into contact with the
main reason why poor mathematicians discourage
the error-detector, from insisting that there is an error,
rather than courage the mistake-maker to learn more:
the discouragers do not want to show disrespect toward
the good mathematician, who made the mistake.
Because of such respect/disrespect tendencies, the
mistake-sweeping process is delayed and development
of mathematics suffers. Why not just focus on math;
here on correcting my sign-error and determining the
domain of convergence? Generalization to other
algebras? Other functions than inv?
Johannes H Andersen
Hope that this does not lead to the same racket in this thread,
this may discougare others to do exactly what you said.
There are so many other threads which deals with whatever
it is about. Please ....
Johannes
Ken Alverson
news:38D4358C...@madasafish.com...
> > > Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
> >
>
> Not a valid counterexample. inv(A) must exist.
Ken
Pertti Lounesto
> "Johannes H Andersen" <jo...@madasafish.com> wrote:
>
> > > > Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
> > >
> > > Wrong (in general). Let A=0 and B=1.
> >
> > Not a valid counterexample. inv(A) must exist.
> Easy enough to fix. Let A=-1 and B=1.
Not valid, because inv(A+B) was supposed to exist.
Doug Norris
>Exactly. And you came here into contact with the
>main reason why poor mathematicians discourage
>the error-detector, from insisting that there is an error,
>rather than courage the mistake-maker to learn more:
>the discouragers do not want to show disrespect toward
>the good mathematician, who made the mistake.
Revisionist history lesson #21: If someone catches a mistake you make, you
then claim that you made the mistake "on purpose", as a psychology experiment.
Pertti, try something else - this is old.
Doug
Randy Yates
>
> Randy Yates wrote:
> >
> > Pertti Lounesto wrote:
> > >
> > > Virgil wrote:
> > >
> > > > "Brett George" <b.ge...@clarityeq.com> wrote:
> > > >
> > > > >Is there a method (or identity) in which you could solve the matrix problem
> > > > >inv(A+B), in terms of A,B,inv(A) and inv(B)?
> > > > >
> > > > >I need this because inv(A) and inv(B) are easy to solve, while there sum is
> > > > >not.
> > > >
> > > > The existence of inv(A) and inv(B) is no guarantee that there will be a
> > > > matrix inv(A+B).
> > > >
> > > > of A,B,inv(A) and inv(B).
> > >
> >
> > Wrong (in general). Let A=0 and B=1.
>
> Not a valid counterexample. inv(A) must exist.
I stand corrected. I am not used to proofs which span multple posts!
Pertti Lounesto
> Ken Alverson wrote:
> >
> > "Johannes H Andersen" <jo...@madasafish.com> wrote in message
> > news:38D4358C...@madasafish.com...
> > > > > Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
> > > >
> > > > Wrong (in general). Let A=0 and B=1.
> > >
> > > Not a valid counterexample. inv(A) must exist.
> > Easy enough to fix. Let A=-1 and B=1.
> >
> > Ken
>
> There is the constraint about existence of A, B, A', and B'. Even after
> fixing the sign mistake, the series clearly fails for A=B=1. But, others
> have already beat down the blunder about convergence considerations.
> A=1, B=2 fails horribly, because of failure to consider convergence.
>
> Lynn Killingbeck (nominated kook)
Only a kook cannot evaluate the significance of a mistake.
Here is classification of math-mistakes:
1. Cutting corners: The mistake-maker knows what is right,
but makes an error deliberately, to smooth his presentation.
2. Carelesness: The mistake-maker knows what is right,
but does not focus enough attention and makes a mistake.
3. Ignorance: The mistake-maker just does not care about
knowing the details.
4. Overconfidence: The mistake-maker is proud of his skills
and makes a mistake about a well-known detail.
5. Non-charted territory: An explorer does not yet have an
accurate cognitive chart about the domain to be explored
by the collectivity of mathematicians, and is mistaken.
Your jubilation about errors of type 1 and 2, shows that you
have never committed a mistake of type 5.
Jerry Avins
>
> Lynn Killingbeck wrote:
>
> > Ken Alverson wrote:
> > >
> > > "Johannes H Andersen" <jo...@madasafish.com> wrote in message
> > > news:38D4358C...@madasafish.com...
> > > > > > Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
> > > > >
> > > > > Wrong (in general). Let A=0 and B=1.
> > > >
> > > > Not a valid counterexample. inv(A) must exist.
> > > Easy enough to fix. Let A=-1 and B=1.
> > >
> > > Ken
> >
> > There is the constraint about existence of A, B, A', and B'. Even after
> > fixing the sign mistake, the series clearly fails for A=B=1. But, others
> > have already beat down the blunder about convergence considerations.
> > A=1, B=2 fails horribly, because of failure to consider convergence.
> >
> > Lynn Killingbeck (nominated kook)
>
> Only a kook cannot evaluate the significance of a mistake.
> Here is classification of math-mistakes:
>
> 1. Cutting corners: The mistake-maker knows what is right,
> but makes an error deliberately, to smooth his presentation.
This is commonly called "lying".
> 2. Carelesness: The mistake-maker knows what is right,
> but does not focus enough attention and makes a mistake.
, often more than once.
> 3. Ignorance: The mistake-maker just does not care about
> knowing the details.
Not caring about mere detail is commonly called "arrogance".
> 4. Overconfidence: The mistake-maker is proud of his skills
> and makes a mistake about a well-known detail.
Overconfidence often leads to carelessness.
> 5. Non-charted territory: An explorer does not yet have an
> accurate cognitive chart about the domain to be explored
> by the collectivity of mathematicians, and is mistaken.
Arrogance and overconfidence lead some writers to forget when they
should express themselves tentatively. This too happens to most of us
sooner or later.
>
> Your jubilation about errors of type 1 and 2, shows that you
> have never committed a mistake of type 5.
Many of us derive genuine joy from putting down people who delight in
putting down others by writing "Wrong."
Let's keep hearing from you!
Jerry
--
Engineering is the art of making what you want from things you can get.
-----------------------------------------------------------------------
Jerry Avins
>
> ...
>
> Lynn Killingbeck (nominated kook)
With an epithet like that, you get my vote!
Rob Johnson
>>
>> > > > Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
>> > >
>> > > Wrong (in general). Let A=0 and B=1.
>> >
>> > Not a valid counterexample. inv(A) must exist.
>> Easy enough to fix. Let A=-1 and B=1.
>
In article <9533435...@mel.ihug.com.au>,
"Brett George" <b.ge...@clarityeq.com> wrote:
>Is there a method (or identity) in which you could solve the matrix problem
>inv(A+B), in terms of A,B,inv(A) and inv(B)?
I don't see anywhere that inv(A+B) is assumed to exist. The question is
asking for a method to compute inv(A+B) from A, B, inv(A), and inv(B).
Presumably, if inv(A+B) did not exist, the method would say that.
However, the question itself does not presume that inv(A+B) exists.
Without further constraints, even after fixing up the alternating signs
of the terms, there are many cases in which the formula above fails,
even though inv(A+B) and the other required quantities exist. In my
previous post on this topic, <8avkl9$5...@nnrp2.farm.idt.net>, I
discussed a formula similar to yours, and showed one such case in which
it failed. One constraint that would allow your formula to work, after
fixing up the alternating signs of the terms, would be to require the
spectral radius of B inv(A) be less than 1. However, this constraint is
not easy to get around. For example scaling A and B has no effect on
the spectral radius of B inv(A).
Rob Johnson
robj...@idt.net
Doug Norris
>Indeed, many of you in sci.math are low-minded put-
>downers, for whom mathematics is a means to boost
>one's ego, ^^^^^
^^^^^^^^^
Seems to me that you'd be an expert on this.
Doug
Pertti Lounesto
> Pertti Lounesto wrote:
>
> > Here is classification of math-mistakes:
> >
> > 1. Cutting corners: The mistake-maker knows what is right,
> > but makes an error deliberately, to smooth his presentation.
>
> This is commonly called "lying".
No. A presentation often necessitates simplification,
and gauging the text to the intended audience.
> > 2. Carelesness: The mistake-maker knows what is right,
> > but does not focus enough attention and makes a mistake.
>
> , often more than once.
>
> > 3. Ignorance: The mistake-maker just does not care about
> > knowing the details.
>
> Not caring about mere detail is commonly called "arrogance".
Rather it is lack of motivation and interest. Ignorant people
just aim lower than you, in math, because they have other
interests.
> > 4. Overconfidence: The mistake-maker is proud of his skills
> > and makes a mistake about a well-known detail.
>
> Overconfidence often leads to carelessness.
No. A careless writer knows that there is a chance that
he makes a mistake, while he writes quickly. Somebody,
who is overconfident about his math skills, is driven by
curiosity to new territories, where his present skills are
not sufficient, and then makes a mistake without being
aware of it. Misjudgement of complexity (of a known
topic) is overconfidence.
> > 5. Non-charted territory: An explorer does not yet have an
> > accurate cognitive chart about the domain to be explored
> > by the collectivity of mathematicians, and is mistaken.
>
> Arrogance and overconfidence lead some writers to forget when they
> should express themselves tentatively. This too happens to most of us
> sooner or later.
True, but not related to my class 5, which is the most
significant type of math-mistakes. For more information
about class 5 math-mistakes, see
http://www.hit.fi/~lounesto/counterexamples.htm
> Many of us derive genuine joy from putting down people
> who delight in putting down others by writing "Wrong."
Indeed, many of you in sci.math are low-minded put-
downers, for whom mathematics is a means to boost
one's ego, and not a source of inspiration of new ideas.
Brett George
you can assume inv(A+B), inv(A) and inv(B) exist.
An example would be where A is toeplitz, and B is a diaganol matrix.
so inv(A) is O(N(log2N)^2) and inv(B) is O(N) but inv(A+B) is,
unfortanately, O(N^3).
Brett.
"Brett George" <b.ge...@clarityeq.com> wrote in message
news:9533435...@mel.ihug.com.au...
> Is there a method (or identity) in which you could solve the matrix
problem
> inv(A+B), in terms of A,B,inv(A) and inv(B)?
>
> I need this because inv(A) and inv(B) are easy to solve, while there sum
is
> not.
>
> Thanks in advance.
>
> Brett
>
>
Pertti Lounesto
> Rob Johnson wrote:
> >
> > In article <38D525E5...@hit.fi>,
> > Pertti Lounesto <Pertti....@hit.fi> wrote:
> > >Ken Alverson wrote:
> > >
> > >> "Johannes H Andersen" <jo...@madasafish.com> wrote:
> > >>
> > >> > > > Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
> > >> > >
> > >> > > Wrong (in general). Let A=0 and B=1.
> > >> >
> > >> > Not a valid counterexample. inv(A) must exist.
> > >> Easy enough to fix. Let A=-1 and B=1.
> > >
> > >Not valid, because inv(A+B) was supposed to exist.
> >
> > In article <9533435...@mel.ihug.com.au>,
> > "Brett George" <b.ge...@clarityeq.com> wrote:
> > >Is there a method (or identity) in which you could solve the matrix problem
> > >inv(A+B), in terms of A,B,inv(A) and inv(B)?
> >
> > I don't see anywhere that inv(A+B) is assumed to exist. The question is
> > asking for a method to compute inv(A+B) from A, B, inv(A), and inv(B).
> > Presumably, if inv(A+B) did not exist, the method would say that.
> > However, the question itself does not presume that inv(A+B) exists.
> >
> > Without further constraints, even after fixing up the alternating signs
> > of the terms, there are many cases in which the formula above fails,
> > even though inv(A+B) and the other required quantities exist. In my
> > previous post on this topic, <8avkl9$5...@nnrp2.farm.idt.net>, I
> > discussed a formula similar to yours, and showed one such case in which
> > it failed. One constraint that would allow your formula to work, after
> > fixing up the alternating signs of the terms, would be to require the
> > spectral radius of B inv(A) be less than 1. However, this constraint is
> > not easy to get around. For example scaling A and B has no effect on
> > the spectral radius of B inv(A).
> >
> > Rob Johnson
> > robj...@idt.net
>
> My own intuition is that, if there is some norm N() such that N(B)<N(A),
> then the technique converges. If the strict inequality is the other
> direction, interchange A<->B. If N(A)=N(B), I give up. All by analogy to
> the expansion of 1/(1+x)=1-x+x^2-x^3+-... converging for |x|<1.
What is wrong with N(B/A) being the spectral radius or largest
of the absolute values of the eigenvalue of B/A (as proposed by
Rob Johnson and Johannes Andersen)?
Randy Yates
>
> In article <38D525E5...@hit.fi>,
> Pertti Lounesto <Pertti....@hit.fi> wrote:
> >Ken Alverson wrote:
> >
> >> "Johannes H Andersen" <jo...@madasafish.com> wrote:
> >>
> >> > > > Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
> >> > >
> >> > > Wrong (in general). Let A=0 and B=1.
> >> >
> >> > Not a valid counterexample. inv(A) must exist.
> >> Easy enough to fix. Let A=-1 and B=1.
> >
> >Not valid, because inv(A+B) was supposed to exist.
>
> In article <9533435...@mel.ihug.com.au>,
> "Brett George" <b.ge...@clarityeq.com> wrote:
> >Is there a method (or identity) in which you could solve the matrix problem
> >inv(A+B), in terms of A,B,inv(A) and inv(B)?
>
> I don't see anywhere that inv(A+B) is assumed to exist.
Perhaps the previous articles haven't all reached you? Here
is a cut and paste from my post:
Pertti Lounesto wrote:
>
> Virgil wrote:
>
> > "Brett George" <b.ge...@clarityeq.com> wrote:
> >
> > >Is there a method (or identity) in which you could solve the matrix problem
> > >inv(A+B), in terms of A,B,inv(A) and inv(B)?
> > >
> > >I need this because inv(A) and inv(B) are easy to solve, while there sum is
> > >not.
> >
> > The existence of inv(A) and inv(B) is no guarantee that there will be a
> > matrix inv(A+B).
> >
> > Even if inv(A+B) exists, there is no general way to express it in terms
> > of A,B,inv(A) and inv(B).
>
> Wrong. inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
--
Brett George
Also see my other mail for additional information.
In my case (AB)=(BA)', which follows the A=A' property of toeplitz
matricies.
Brett.
"Joe Skrap" <sk...@hotmail.com> wrote in message
news:nbb5rh...@forum.mathforum.com...
Ray Andraka
on two different shoes as I was heading out for a full day of classes. Of course,
the only one who noticed (or at least was bold enough to say anything) all day was
an ex-girlfriend, so yes, it became an instant psychology class experiment. The
scary part was that I didn't notice that one shoe was black and one was white
until halfway through my second class.
Doug Norris wrote:
>
> Revisionist history lesson #21: If someone catches a mistake you make, you
> then claim that you made the mistake "on purpose", as a psychology experiment.
>
> Pertti, try something else - this is old.
>
> Doug
--
-Ray Andraka, P.E.
President, the Andraka Consulting Group, Inc.
401/884-7930 Fax 401/884-7950
email rand...@ids.net
http://users.ids.net/~randraka
Neil Judell
caffeine consumption? Reminds me of an event
I witnessed as an undergrad lo many many years ago.
Two math profs (math logic/set theory/saturated model theory) met in the
stairwell. Discussed this that and the other for
about ten minutes. At the end of the discussion, one said to the other:
"Pardon me, Gerry, but do you recall whether I
was going upstairs or coming downstairs?" Second prof replied "Gene, I
believe you were going upstairs." First retorted:
"Oh good, that means I've eaten my lunch."
May the gods protect me from becoming like that...
"Ray Andraka" <rand...@ids.net> wrote in message
news:38D5D334...@ids.net...
Pertti Lounesto
elements of inv(A+B) are 1/2.
Rob Johnson
Pertti Lounesto <Pertti....@hit.fi> wrote:
>Prove that if A = I and -1 is not an eigenvalue of B, the diagonal
>elements of inv(A+B) are 1/2.
I seem to be having trouble with the case B = [[2 0][0 3]].
Rob Johnson
robj...@idt.net
Gordon Sande
<Pertti....@hit.fi> wrote:
>Prove that if A = I and -1 is not an eigenvalue of B, the diagonal
>elements of inv(A+B) are 1/2.
A = I
B = 1/2 I, all eigenvalues are 1/2
A+B = 3/2 I
inv(A+B) = 2/3 I, with all diagonal values 2/3 (which is not 1/2)
Even this trivial case is a counter example!
Pertti Lounesto
> Pertti Lounesto <Pertti....@hit.fi> wrote:
>
> >Prove that if A = I and -1 is not an eigenvalue of B, the diagonal
> >elements of inv(A+B) are 1/2.
>
> A = I
> B = 1/2 I, all eigenvalues are 1/2
> A+B = 3/2 I
> inv(A+B) = 2/3 I, with all diagonal values 2/3 (which is not 1/2)
>
> Even this trivial case is a counter example!
Your counterexample raises the question: how to deform
the assuptions, so as to make the conclusion hold? How
about adding the condition: B in SO(n)? So, prove that if
A = I and -1 is not an eigenvalue of B in SO(n), then the
Pertti Lounesto
> Revisionist history lesson #21: If someone catches a mistake you make, you
> then claim that you made the mistake "on purpose", as a psychology experiment.
>
> Pertti, try something else - this is old.
OK. Last week I visited a playground, where there
were 5 children playing. I counted the children aloud:
1,2,3,5,6. The children were excited and shouted:
wrong, wrong! Doug shouted: you missed 4. David
added: you counted 5 twice. I admitted that I was
wrong.
Then I said: inv(A+B) = inv(A)+inv(A) B inv(A)+...
The children continued their playing and said that
they are not interested: no one cares!
Doug Norris
>Prove that if A = I and -1 is not an eigenvalue of B, the diagonal
>elements of inv(A+B) are 1/2.
Pertti, why would we prove something that's obviously false?
Counterexample: Let A=I, and let B={{5,0},{0,4}}
Then A+B = {{6,0},{0,5}}
and inv(A+B) = {{1/6,0},{0,1/5}} //
Now you can go ahead and claim that either
1) Pertti's mistakes aren't important.
2) This was a psychology experiment.
3) This was a mistake of Type I, and therefore not important.
4) This was a mistake of Type II, and therefore not important.
Once you've made your choice, please enter it here: _______
Doug
Doug Norris
>Your counterexample raises the question: how to deform
>the assuptions, so as to make the conclusion hold? How
>about adding the condition: B in SO(n)? So, prove that if
>A = I and -1 is not an eigenvalue of B in SO(n), then the
>diagonal elements of inv(A+B) are 1/2.
How about, instead, getting it right in the first place?
Remember: Pertti's mistakes aren't important.
Doug
Jerry Avins
>
> Jerry Avins wrote:
>
> > Pertti Lounesto wrote:
> >
> > > Here is classification of math-mistakes:
> > >
> > > 1. Cutting corners: The mistake-maker knows what is right,
> > > but makes an error deliberately, to smooth his presentation.
> >
> > This is commonly called "lying".
>
> No. A presentation often necessitates simplification,
> and gauging the text to the intended audience.
I reject that. Simplification without notification, especially in a
technical exposition, is concealment of truth.
>
> > > 2. Carelesness: The mistake-maker knows what is right,
> > > but does not focus enough attention and makes a mistake.
> >
Text got lost here:
> > , often more than once.
It was originally
This has happened to most of us, often more than once.
> >
> > > 3. Ignorance: The mistake-maker just does not care about
> > > knowing the details.
> >
> > Not caring about mere detail is commonly called "arrogance".
>
> Rather it is lack of motivation and interest. Ignorant people
> just aim lower than you, in math, because they have other
> interests.
Presuming to instruct others without the care necessary to reach their
level of competence, while believing that you have something interesting
to say: that is arrogance indeed. Don't dig yourself in deeper.
I don't know the general tenor of sci.math; I have never visited that
group. Here on comp.dsp (with rare exceptions), respondents tend to be
helpful and supportive, and we point out each other's errors (or
supposed errors) with tact and reasonable restraint. It may be only
chance coincidence, but sum (brashness+competance) and the ratio
(modesty/experience) are remarkably constant.
Jerry Avins
When my oldest son first learned to count, he would have said "1, 1, 1,
1, 1", paused, and announced "5!" (If there had been a Siamese twin, he
might have said "1, 2, 1, 1" before announcing "5!" When he was about 26
months old, I taught him this trick: "If you name each one in turn with
the next counting number, then the name of the last one will be the
number of the group." My guess is that you would have "corrected" him
early on, perhaps destroying his mathematical intuition. (Number one son
went on to major in statistics.)
Jerry Avins
>
...
>
> Remember: Pertti's mistakes aren't important.
>
> Doug
I don't dispute that. Interestingly, it implies that his successes
aren't either.
Johannes H Andersen
Pertti Lounesto wrote:
>
> Doug Norris wrote:
>
> > Revisionist history lesson #21: If someone catches a mistake you make, you
> > then claim that you made the mistake "on purpose", as a psychology experiment.
> >
> > Pertti, try something else - this is old.
>
> OK. Last week I visited a playground, where there
> were 5 children playing. I counted the children aloud:
> 1,2,3,5,6. The children were excited and shouted:
> wrong, wrong! Doug shouted: you missed 4. David
> added: you counted 5 twice. I admitted that I was
> wrong.
>
> Then I said: inv(A+B) = inv(A)+inv(A) B inv(A)+...
> The children continued their playing and said that
> they are not interested: no one cares!
But you, yourself relish in shouting "Wrong" or "No!" instead
of politely suggest a correction or improvement. I think
this is what people don't like.
Johannes (the unwashed child)
Randy Yates
> Pertti Lounesto wrote:
> [...]
> But you, yourself relish in shouting "Wrong" or "No!" instead
> of politely suggest a correction or improvement. I think
> this is what people don't like.
Bingo.
--
Randy Yates
DSP Engineer
Ericsson / Research Triangle Park, NC, USA
qus...@rtp.ericsson.se, 919-472-1124
Jeff Stuart
If you choose to engage in this "conversation" with Dr. Lounesto,
you need to understand that he has made a second career out of
haranging newsgroups about errors and what he interprets as
errors in mathematical papers. While his primary interest is
in Clifford algebras, his secondary interest is apparently finding
minor bugs in algebraic papers so that he can send the authors
detailed notes in which he kindly includes a copy of the incorrect
result (as he sees it) on which he has politely printed "WRONG"
in large, red letters. What this would suggest is that his formidable
mathematical skills are matched by his formidable ego. Perhaps
you should also be aware that he has apparently become annoyed
that folks on the math.sci newsgroup have largely ignored him,
and that he is trolling for another mathematical community that might
be more willing to play his game. If you engage him, you only
encourage him.
Jeff Stuart
Dik T. Winter
> Even if inv(A+B) exists, there is no general way to express it in terms
> of A,B,inv(A) and inv(B).
As a reply you wrote:
> Wrong.
You were shown to be wrong, but you have given a classification for
math mistakes:
> 1. Cutting corners: The mistake-maker knows what is right,
> but makes an error deliberately, to smooth his presentation.
> 2. Carelesness: The mistake-maker knows what is right,
> but does not focus enough attention and makes a mistake.
> 3. Ignorance: The mistake-maker just does not care about
> knowing the details.
> 4. Overconfidence: The mistake-maker is proud of his skills
> and makes a mistake about a well-known detail.
> 5. Non-charted territory: An explorer does not yet have an
> accurate cognitive chart about the domain to be explored
> by the collectivity of mathematicians, and is mistaken.
> Your jubilation about errors of type 1 and 2, shows that you
> have never committed a mistake of type 5.
Under what class falls the use of the word "wrong" (in that word you
did disqualify Virgil as being inadequate in this case.)
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
Ray Andraka
Neil Judell wrote:
> Ray -- were you simply unobservant, or was there a problem with insufficient
> caffeine consumption? Reminds me of an event
> I witnessed as an undergrad lo many many years ago.
>
Actually, I think it was a case of over-consumption of another beverage the
night before. Lehigh was like that back then.
>
> Two math profs (math logic/set theory/saturated model theory) met in the
> stairwell. Discussed this that and the other for
> about ten minutes. At the end of the discussion, one said to the other:
> "Pardon me, Gerry, but do you recall whether I
> was going upstairs or coming downstairs?" Second prof replied "Gene, I
> believe you were going upstairs." First retorted:
> "Oh good, that means I've eaten my lunch."
>
> May the gods protect me from becoming like that...
>
> "Ray Andraka" <rand...@ids.net> wrote in message
> news:38D5D334...@ids.net...
> > Reminds me of a day when I was an undergrad at Lehigh. I somehow managed
> to put
> > on two different shoes as I was heading out for a full day of classes. Of
> course,
> > the only one who noticed (or at least was bold enough to say anything) all
> day was
> > an ex-girlfriend, so yes, it became an instant psychology class
> experiment. The
> > scary part was that I didn't notice that one shoe was black and one was
> white
> > until halfway through my second class.
> >
> > Doug Norris wrote:
> >
> > >
> > > Revisionist history lesson #21: If someone catches a mistake you make,
> you
> > > then claim that you made the mistake "on purpose", as a psychology
> experiment.
> > >
> > > Pertti, try something else - this is old.
> > >
Pertti Lounesto
> Pertti Lounesto wrote:
> >
> > Doug Norris wrote:
> >
> > > Revisionist history lesson #21: If someone catches a mistake you make, you
> > > then claim that you made the mistake "on purpose", as a psychology experiment.
> > >
> > > Pertti, try something else - this is old.
> >
> > OK. Last week I visited a playground, where there
> > were 5 children playing. I counted the children aloud:
> > 1,2,3,5,6. The children were excited and shouted:
> > wrong, wrong! Doug shouted: you missed 4. David
> > added: you counted 5 twice. I admitted that I was
> > wrong.
> >
> > Then I said: inv(A+B) = inv(A)+inv(A) B inv(A)+...
> > The children continued their playing and said that
> > they are not interested: no one cares!
>
> But you, yourself relish in shouting "Wrong" or "No!" instead
> of politely suggest a correction or improvement. I think
> this is what people don't like.
It is ineffective not to be forthright in exposing mistake-
makers, who relish hatching misconceptions, in particular,
when the forum is full of mistake-makers, who engage in
mistakes at an elementary level, like in sci.math. If you are
not frank, the mistake-maker often interpretes that you are
just pointing out some interpretational linguistic inaccuracy
instead of correcting a major miscomprehension.
To be specific, Virgil had a misconseption about existence
of a general formula to express inv(A+B) in terms of A, B,
inv(A) and inv(B). In terms of 2x2-matrices, in Mat(2,R),
Virgil's miscomprehesion can be analyzed as follows.
Is there a non-trivial (= not something like inv(A+B) =
inv(inv(inv(A))+inv(inv(B))) formula, for which
inv(A+B) = expression(A,B,inv(A),inv(B))
for
1. all invertible A,B for which A+B is invertible,
2. all A,B in some domain of dimension 3 in Mat(2,R),
3. all A,B on some surface of dimension 2 in Mat(2,R),
4. particular isolated matrices A,B in Mat(2,R).
Formulas of type 1 and 2 are called general, in general.
Formulas of type 3 and 4 are considered special, not
general. Virgil had a misconception that no type 2
formula exist. I corrected that misconceptions, and
made a valuable contribution to the cognitive developent
of Virgil.
My correction, inv(A+B) = inv(A) - inv(A) B inv(A) +-...,
contained a sign error, which some contributors relished,
although Virgil was certainly able to correct it himself.
Many posters gave a counterexample in the case 1 to
my formula of the case 2, and thus showed poor ability
to evaluate cognition of other posters. Those posters were
counterproductive in serving Virgil: they confused him.
In evaluating cognition of mistake-makers, the following
cases ought to be distinguished:
1. the mistake-maker knows the right thing, that is, the
error is only a misprint or he was cutting corners,
2. the mistake-maker is mistaken, but other participants
in the forum know the right thing,
3. the mistake-maker is mistaken, other participants do not
know the right thing, but the thing is generally known,
4. no one knows the right thing, except the error-detector.
Johannes, I am probably the most experienced error-exposer
in the whole wide world (= www) in regards of detecting
mistakes of type 4. In the case 4, the error-exposer must
be truely frank about there being mistakes, while there is
nobody to agree with about existence of a possible mistake.
If you are further interested in how to forthright and frank
in correcting advanced mistake-makers, point your browser
to http://www.hit.fi/~lounesto/counterexamples.htm.
Pertti Lounesto
> If you choose to engage in this "conversation" with Dr. Lounesto,
> you need to understand that he has made a second career out of
> haranging newsgroups about errors and what he interprets as
> errors in mathematical papers.
It is not my interptetaion alone. The mistake-makers themselves
as well as experts in the field consider my counterexamples valid.
You might have verified this by reading
P. Lounesto: Counterexamples in Clifford algebras, "Advances in
Applied Clifford Algebras" 6 (1996), 69-104,
where the editorial board of "Advances in Applied Clifford Algebras"
consists of 10 mathematicians, 7 of which listed as mistake-makers
in my paper.
> While his primary interest is
> in Clifford algebras, his secondary interest is apparently
> finding minor bugs in algebraic papers
You presented invalid argument, the type of invalidity being
numbered as 3 and 4 in my list of invalid arguments,
http://www.hit.fi/~lounesto/sci.math.htm,
against my list of counterexamples,
http://www.hit.fi/~lounesto/counterexamples.htm.
The reason for you to present such invalid argument, is the
fact that you project my text down to your own experiences
of catching poor mathematicians of making insiginicant errors.
Such a downgrading misinterpretation of my counterexamples,
based on limited experiences of the downgrader, has been
presented often here in sci.math, most notably by Robin
Chapman, who enforced his downgrading by challenging me
to a math-competition of proving his theorems. Chapman
not only arrived as a non-winner of his own challenge, but
also made a math-mistake at the topic of his own challenge,
http://www.hit.fi/~lounesto/Robin.Chapman
http://www.hit.fi/~lounesto/mistake
Now it seems that Jeff Stuart want to join Chapman as a
user of invalid argument of type 7a, in my list,
http://www.hit.fi/~lounesto/sci.math.htm
> so that he can send the authors
> detailed notes in which he kindly includes a copy of the incorrect
> result (as he sees it) on which he has politely printed "WRONG"
> in large, red letters. What this would suggest is that his formidable
> mathematical skills are matched by his formidable ego.
Here you engage in using invalid argument of type 0, of
http://www.hit.fi/~lounesto/sci.math.htm
> If you engage him, you only encourage him.
Jeff, as long as you do not have your own experience
about catching renowned mathematicians of mistake-making,
you will continue to misinterprete anything by your limited
experiences based on catching poor mathematicians of
making low-level errors.
Johannes H Andersen
Pertti Lounesto wrote:
> Doug Norris wrote:
>
> > Revisionist history lesson #21: If someone catches a mistake you make, you
> > then claim that you made the mistake "on purpose", as a psychology experiment.
> >
> > Pertti, try something else - this is old.
>
> OK. Last week I visited a playground, where there
> were 5 children playing. I counted the children aloud:
> 1,2,3,5,6. The children were excited and shouted:
> wrong, wrong! Doug shouted: you missed 4. David
> added: you counted 5 twice. I admitted that I was
> wrong.
>
> Then I said: inv(A+B) = inv(A)+inv(A) B inv(A)+...
> The children continued their playing and said that
> they are not interested: no one cares!
Another thing worth noting: Children may be noisy an
unwashed, but only for a short while. Their rate of
perception is astonishingly quick, and before you know
it, they have learned all what we know and even more.
Johannes
Johannes H Andersen
Pertti Lounesto wrote:
> Johannes H Andersen wrote:
>
> > Pertti Lounesto wrote:
> > >
> > > Doug Norris wrote:
> > >
> > > > Revisionist history lesson #21: If someone catches a mistake you make, you
> > > > then claim that you made the mistake "on purpose", as a psychology experiment.
> > > >
> > > > Pertti, try something else - this is old.
> > >
> > > OK. Last week I visited a playground, where there
> > > were 5 children playing. I counted the children aloud:
> > > 1,2,3,5,6. The children were excited and shouted:
> > > wrong, wrong! Doug shouted: you missed 4. David
> > > added: you counted 5 twice. I admitted that I was
> > > wrong.
> > >
> > > Then I said: inv(A+B) = inv(A)+inv(A) B inv(A)+...
> > > The children continued their playing and said that
> > > they are not interested: no one cares!
> >
I am sorry to have to say that you are now twisting the argument.
Virgil said:
>>>>>The existence of inv(A) and inv(B) is no guarantee that
>>>>>there will be a matrix inv(A+B).
>>>>>Even if inv(A+B) exists, there is no general way to express
>>>>>it in terms of A,B,inv(A) and inv(B).
The original poster did not specify the domain, but this frequently
happens for posters who just want a tip for a practical solution to
a problem. We frequently have to do some gueswork about the posters
intensions. Hence, was certainly not unreasonalbe to assume that the
domain for this context was Mat(n,R).
In this context, "general" does not mean "in some domain", so Virgil
was correct in his assertion.
Do you really take "general" to mean "some domain" but not all
domains in Mat(n,R) ?
I know you said "general, in general" , but if this works for you
then you should be a politician.
Virgil deserves better than that, his contributions in this group
are always interesting and well informed.
Johannes
Pertti Lounesto
> Another thing worth noting: Children may be noisy an
> unwashed, but only for a short while. Their rate of
> perception is astonishingly quick, and before you know
> it, they have learned all what we know and even more.
True, and they also focus on more essential things, than
mathematics, regarding cost-benefit aspects in their lives.
> But you, yourself relish in shouting "Wrong" or "No!"
> instead of politely suggest a correction or improvement.
Here is an anecdote of politeness. I once falsified a theorem
of a leading mathematician of a European country (good
in mathematics, but the country is not important). I sent
him a letter, which contained a counterexample to his
theorem. He answered my letter, with the understanding
that I was congratulating him of his theorem. I sent a new
letter, explicitly mentioning that the proof contained a gap,
because I had a counterexample (I enclosed a new and
simpler counterexample). The academician sent me a
letter thanking me of my interest to his theorem, this time
evidently pretending that he did not understand the
purpose of my letter. I sent again a new letter, with
explicit statement that his theorem is false, because I
have a counterexample (again a new, and still simpler).
The academician responded by proposing me to write
a paper with him about developing his theorem further.
I responded, without commenting on the proposed
collaboration, that his theorem is wrong, by enclosing
a photocopy of the false theorem and encircling the
erroneous parts by red colour and writing in the margin
WRONG, in capital letters, and repeated my counter-
example. The academician answered, --- well it is
another story.
Johannes H Andersen
Johannes H Andersen wrote:
> The original poster did not specify the domain, but this frequently
> happens for posters who just want a tip for a practical solution to
> a problem. We frequently have to do some gueswork about the posters
> intensions. Hence, was certainly not unreasonalbe to assume that the
> domain for this context was Mat(n,R).
> ............
A possible confusion here:
I gather from your post that you may be using Mat(n,R) to mean
tensors of order n over R, such that Mat(2,R) are the matrices,
Mat(1,R) the vectors.
In my reply I, was using Mat(n,R) to mean square matrices over R of
size n, ( any n > 0 ) . This came about because I did not spot the
details of your implied definition.
I just wanted to clear this up so that we know what we are talking
about. I am quite happy with your meaning of Mat(n,R) if I
understand it correctly.
Johannes
Jeff Stuart
ego and if you apply your shallow and self-inflating psycho-analysis to
everyone around you, I would suppose that you have (1) no loving family,
(2) no long term friends, (3) no welcoming colleagues. It is rather audacious
for you to conclude that I have no experience working with excellent
mathematicians and their mistakes merely because I disagree with your
approach to errors in the work of others. Unlike you, I have a view of
mathematics that does not include mocking, confrontational tactics, but
then again, I have not declared myself to be the world's expert in counter-
examples merely because I have a bunch of books in my library on the
subject. (Gee, maybe I should since I own almost half of the books you cite!)
Actually, I regularly deal with errors made by famous and important
mathematicians - that is part of the natural give and take of doing research
with them. Also, as a long time referee for one of the major journals in my
field, I have regularly been in the position of informing others of their errors
or possible errors.
>The reason for you to present such invalid argument, is the
>fact that you project my text down to your own experiences
>of catching poor mathematicians of making insiginicant errors.
>Such a downgrading misinterpretation of my counterexamples,
>based on limited experiences of the downgrader, has been
>presented often here in sci.math, most notably by Robin
>Chapman, who enforced his downgrading by challenging me
>to a math-competition of proving his theorems. Chapman
>not only arrived as a non-winner of his own challenge, but
>also made a math-mistake at the topic of his own challenge,
>
And what kind of invalid argument is it when you cite another
mathematician's name in an attempt to raise yourself by some
sort of self-measured comparison?
>> so that he can send the authors
>> detailed notes in which he kindly includes a copy of the incorrect
>> result (as he sees it) on which he has politely printed "WRONG"
>> in large, red letters. What this would suggest is that his formidable
>> mathematical skills are matched by his formidable ego.
>
>Here you engage in using invalid argument of type 0, of
Actually, Pertti, I challenge you to find a counterexample to the facts
in the above statement. Do you deny that you report on your own
web site that you send authors detailed correction to their results
along with copies of their papers where you have writtin "WRONG"
marked in large, red letters on the incorrect results? Or do you deny
that you have formidable mathematical skills? Or is it only that you
think that your confrontational, abrasive style is a reflection of modesty?
>
>Jeff, as long as you do not have your own experience
>about catching renowned mathematicians of mistake-making,
>you will continue to misinterprete anything by your limited
>experiences based on catching poor mathematicians of
>making low-level errors.
>
See my comment above. I appreciate your conclusion based on
a single letter that I have only limited experiences, all involving
poor mathematicians and low-level errors. I only hope that
your mathematics is better than (1) your manners, (2) your
ability to analyze people based on a single note (3) your ability
to speculate about other people's professional experiences,
(4) your sense of humility.
If you wonder why you are the victim of so many ad-hominim attacks,
perhaps you should apply a little of your overly quick and overly
hostile analysis to your own behavior towards others.
Jeff Stuart
Pertti Lounesto
> Alright, Pertti,
Jeff, you make several assumptions about me, my
activities and my mathematics, all of which do not
hold, but maybe reflect something of your life.
> I'll let you bait me into a response. You have an amazing
> ego and if you apply your shallow and self-inflating psycho-analysis to
> everyone around you, I would suppose that you have (1) no loving family,
Why don't you ask my wife and daugthers?
> (2) no long term friends,
Why don't you ask my co-authors, who live in Finland,
Russia, Eastern Europe, Western Europe, South America
and North America (in six states)?
> (3) no welcoming colleagues.
I have written joint papers with 3 colleagues in my present
institute, alone.
> It is rather audacious
> for you to conclude that I have no experience working with excellent
> mathematicians and their mistakes merely because I disagree with your
> approach to errors in the work of others.
You have not published, in refereed journals, any mistakes
of your peers. From this I am entitled to draw my conclusion
about your lack of experience in error-detection.
> Unlike you, I have a view of mathematics
> that does not include mocking, confrontational tactics,
Unlike you, I have collaborators in many countries, and even
many continents. Have I confronted them, or collaborated?
> I have not declared myself to be the world's expert in counter-
> examples merely because I have a bunch of books in my library on the
> subject.
Here you assume, incorrectly, that I just read some books,
found some mistakes, and reported them in my web-page
http://www.hit.fi/~lounesto/counterexamples.htm
You only describe your own experiences of error-detection,
not mine. Many of those whose mistakes are listed in
my web-page, are in positions, where I recommended
them, have written papers, which I recommended to be
published, have learned the topic partly from me, etc.
Jeff, you just express experiences of a consumer of
math, not somebody who has participated in creating
new math.
> (Gee, maybe I should since I own almost half of the books you cite!)
> Actually, I regularly deal with errors made by famous and important
> mathematicians - that is part of the natural give and take of doing research
> with them.
Yes, but you probably mean small insignificant mishaps,
based on your experiences, in contrast to my corrections
of major misconceptions.
> Also, as a long time referee for one of the major journals in my
> field, I have regularly been in the position of informing others
> of their errors or possible errors.
So have I. But have you reported mistakes in refereed
articles? If so, how many? Over 10? Over 50?
> And what kind of invalid argument is it when you cite another
> mathematician's name in an attempt to raise yourself by some
> sort of self-measured comparison?
Here you have committed misinterpretation of type 0,
in my list of "sci.math ventilation of its failure and
frustration to the substitutes of valid arguments", in
http://www.hit.fi/~lounesto/sci.math.htm
You have not presented any new arguments. Your
arguments have been presented 100 times already,
and all have been answered in my web-page.
> >> What this would suggest is that his formidable
> >> mathematical skills are matched by his formidable ego.
> >
> >Here you engage in using invalid argument of type 0, of
>
> Actually, Pertti,
Actually, Jeff, read from my web-page my respond to
your argument, of type 0.
> Or do you deny
> that you have formidable mathematical skills?
Again you assume wrong, because of your lack of
experience. Error-detection ability and creativity
(usually regarded as formidable math skill) are two
different things, and can exist in a person, independent
of each other, unlike you assume. I have a special
talent of detecting significant mistakes in works of
other mathematicians (only in my own field, though),
but this does not even imply that I would be any
better than anybody else to produce correct math
(I am as blind as anybody to my own mistakes).
> I appreciate your conclusion based on a single
> letter that I have only limited experiences, all involving
> poor mathematicians and low-level errors.
Have you published any lists of significant mistakes
of your peers in refereed scientific journals? My
conclusion is not based on your letter, but on the
fact that you have not reported any mistakes of peers.
> I only hope that
> your mathematics is better than (1) your manners,
Why don't you evaluate yourself my mathematics, like
my proof of a theorem a regular poster challenged me
to present, but failed to evaluate, see
http://www.hit.fi/~lounesto/Robin.Chapman
> (2) your ability to analyze people based on a single note
My ability to draw conclusions from a non-existing
list of counterexamples by you to theorems of your
peers.
> (3) your ability
> to speculate about other people's professional experiences,
No speculation. It is easy to check from SCI what you
have published, in refereed journals.
> (4) your sense of humility.
>
> If you wonder why you are the victim of so many ad-hominim attacks,
> perhaps you should apply a little of your overly quick and overly
> hostile analysis to your own behavior towards others.
My analysis of your arguments is not at all quick: I have
heard your arguments 100 times already, and have answered
them in my web-page
http://www.hit.fi/~lounesto/sci.math.htm
where I classify such arguments and misinterpretations, of
sci.math posters.
As for "so many ad-homienm attacks", they are just
false arguments of class 0, as listed in my web-page
Randy Yates
>
> Johannes H Andersen wrote:
>
> > Another thing worth noting: Children may be noisy an
> > unwashed, but only for a short while. Their rate of
> > perception is astonishingly quick, and before you know
> > it, they have learned all what we know and even more.
>
> True, and they also focus on more essential things, than
> mathematics, regarding cost-benefit aspects in their lives.
>
> > But you, yourself relish in shouting "Wrong" or "No!"
> > instead of politely suggest a correction or improvement.
>
Hi Pertti,
I can certainly agree that there are people out there
who are extremely difficult to get to "come clean," but
to *presume* a person is like this when knowing relatively
little about them is, in my opinion, rude. In my opinion,
the time that may be lost in giving an unknown person the
benefit of the doubt is worth the respect it shows to others.
Virgil
johannes...@brunel.ac.uk wrote:
>Virgil deserves better than that, his contributions in this group
>are always interesting and well informed.
>
>
>Johannes
I blush.
--
Virgil
vm...@frii.com
Pertti Lounesto
> Pertti Lounesto wrote:
> > Johannes H Andersen wrote:
> >
> > > But you, yourself relish in shouting "Wrong" or "No!"
> > > instead of politely suggest a correction or improvement.
> >
> > Here is an anecdote of politeness. [...]
>
> Hi Pertti,
>
> I can certainly agree that there are people out there
> who are extremely difficult to get to "come clean," but
> to *presume* a person is like this when knowing relatively
> little about them is, in my opinion, rude. In my opinion,
> the time that may be lost in giving an unknown person the
> benefit of the doubt is worth the respect it shows to others.
From the name of a poster, I know whether or not a poster
knows about Clifford algbras, because it is a specialized topics.
If the poster comments on my math, without understanding it,
conclusions can be drawn about the poster. Curiously, many
posters have commented on the math of my web-pages
http://www.hit.fi/~lounesto/counterexamples.htm
http://www.hit.fi/~lounesto/Robin.Chapman
and used similar expressions as other posters used the day
before. This has been going on for weeks, months, years.
Sci.math expressions occur in waves. What should I say
about such posters occurring in waves?
Pertti Lounesto
> Doug Norris wrote:
> >
> ...
> >
> > Remember: Pertti's mistakes aren't important.
> >
> > Doug
>
> I don't dispute that. Interestingly, it implies that his successes
> aren't either.
I have not revoked my rights to mistake-making.
Jerry is not an expert in my field of speciality and
cannot evaluate my possible success. Doug and
Jerry still are close to school bench, were they
were graded on the basis of mistakes by a teacher,
who knew math better than they did -- from this
they infer, incorrectly, that mistake-makers are
poorer in math than mistak-detectors. For the role
of mistakes in advanced mathematics, see
http://www.hit.fi/~lounesto/counterexamples.htm
Doug & Jerry do not understand why I/(I+B), B in
SO(n), is interesting, but wanted to write follow-ups
on that.
Jerry Avins
I don't know what you should _say_, but it seems to me that you should
_think_ that something about the way you express yourself makes people
want to pick on you. Perhaps you can do something to change that; if
not, you might enjoy a private correspondence with E. Robert Tisdale
<ed...@netwood.net>.
Pertti Lounesto
It is not the _way_ I say it, but _what_ I have to say.
Posters have experience about correcting misconceptions
of students or of pointing out misconceptions of peers,
in the case that the correct matter of fact is known.
No one else has listed mistakes, made there at the frontiers
of advancing research, at the same exent as I have.
Posters interprete my postings by their own experices
(how else could they do), and this invariably leads to
misinterpretation, which I kindly correct (and show that
the same misinterpretation has been presented already
100 times). People attach all kinds of mistinterpretations
to my error-exposing activity, but those misinterpretations
tell nothing about my extivity, they only tell some about
the misinterpreter. I do not believe that there is a _way_
to convey _what_ I say without being misinterpreted.
As you, many posters seem to recommend that I
should communicate my ideas in some other _way_,
in order not to be disregarded. But what is there
wrong in being disregarded by ignorant people who
cannot profit from informative postings? Why should
I care? Care about those who do not want to understand.
There are always some people who can benefit from
my informative postings.
Pertti Lounesto
to the statement: "If U in SO(n) has not eigenvalue -1, then
I/(I+U) has diagonal elements 1/2". From Jerry's and Doug's
failure, I conclude that my statement is correct.
Correctness of my statement above, prompts the following
conjecture: "If u in Spin(n), the universal cover of SO(n),
is not -1, then 1/(1+u) has scalar part 1/2". Do Jerry and
Doug fail again, or can they prove this, or do they drop
this course? Stay tuned.
David C. Ullrich
> [...]
>
> It is not the _way_ I say it, but _what_ I have to say.
Wrong!
Randy Yates
Hi Pertti,
The original question involved only the vector space of
matrices over the complex field. This is presumably
much more limited in scope then Clifford algebras
and also probably much more widely studied.
--
Randy Yates
DSP Engineer
Ericsson / Research Triangle Park, NC, USA
qus...@rtp.ericsson.se, 919-472-1124
.
Pertti Lounesto
> The original question involved only the vector space
> of matrices over the complex field.
I corrected misconception of a responder, Virgil,
in the setting of matrices over the complex field.
> This is presumably much
> more limited in scope then Clifford algebras
> and also probably much more widely studied.
Concerning posters commenting on my math, you
presented views on my evaluation of such posters.
I explained my views, and this explanation brought
in my mathematics, Clifford algebras.
Randy Yates
>
> Randy Yates wrote:
>
> > The original question involved only the vector space
> > of matrices over the complex field.
>
> I corrected misconception of a responder, Virgil,
> in the setting of matrices over the complex field.
>
> > This is presumably much
> > more limited in scope then Clifford algebras
> > and also probably much more widely studied.
>
> Concerning posters commenting on my math, you
> presented views on my evaluation of such posters.
No. I presented views on your evaluation of posters
commenting on the math involving the vector space
of matrices over the complex field, an area of
mathematics much less specialized than Clifford
algebras (i.e., "your" math). I am therefore
asserting that, since this less-specialized field
is studied by a much more general audience, it
is not appropriate for you to assume a lack of
knowledge in this area for a person commenting
on this area of math.
Pertti Lounesto
> Pertti Lounesto wrote:
> >
> > Randy Yates wrote:
> >
> > > The original question involved only the vector space
> > > of matrices over the complex field.
> >
> > I corrected misconception of a responder, Virgil,
> > in the setting of matrices over the complex field.
> >
> > > This is presumably much
> > > more limited in scope then Clifford algebras
> > > and also probably much more widely studied.
> >
> > Concerning posters commenting on my math, you
> > presented views on my evaluation of such posters.
>
> No. I presented views on your evaluation of posters
> commenting on the math involving the vector space
> of matrices over the complex field, an area of
> mathematics much less specialized than Clifford
> algebras (i.e., "your" math). I am therefore
> asserting that, since this less-specialized field
> is studied by a much more general audience, it
> is not appropriate for you to assume a lack of
> knowledge in this area for a person commenting
> on this area of math.
This is false. I would never imagine Virgil to
know anything about Clifford algebras. You
intervented into the discussion by inserting a
quote on me "relishing in shouting wrong" and
then explained me being rude. I responded to
you by explaining why in general posters in
sci.math have similar views than you, and this
explanation brought in Clifford algebra, not my
correction of Virgil's misconception. Now you
have repeatedly presented views on my research
topic, Clifford algebras, which are not accurate,
or are misplaced. Would I be rude, if I would
correct your misplaced views, in detail? Or
would I be unhelpful toward you, if I let you
hold on your views?
Randy Yates
>
> Randy Yates wrote:
>
> > Pertti Lounesto wrote:
> > >
> > > Randy Yates wrote:
> > >
> > > > The original question involved only the vector space
> > > > of matrices over the complex field.
> > >
> > > I corrected misconception of a responder, Virgil,
> > > in the setting of matrices over the complex field.
> > >
> > > > This is presumably much
> > > > more limited in scope then Clifford algebras
> > > > and also probably much more widely studied.
> > >
> > > Concerning posters commenting on my math, you
> > > presented views on my evaluation of such posters.
> >
> > No. I presented views on your evaluation of posters
> > commenting on the math involving the vector space
> > of matrices over the complex field, an area of
> > mathematics much less specialized than Clifford
> > algebras (i.e., "your" math). I am therefore
> > asserting that, since this less-specialized field
> > is studied by a much more general audience, it
> > is not appropriate for you to assume a lack of
> > knowledge in this area for a person commenting
> > on this area of math.
>
> This is false.
*What* is false? I made two assertions above. To which
are you responding? The second? Both? As a mathematician,
I expect you to be clear. The use of such an imprecise
definite article in this context is negligent.
> I would never imagine Virgil to
> know anything about Clifford algebras. You
> intervented into the discussion by inserting a
> quote on me "relishing in shouting wrong" and
> then explained me being rude.
Excuse me? Intervened? As if *my* comments were
not allowed, while those of any other general
poster are? Your attitude is curious.
> I responded to
> you by explaining why in general posters in
> sci.math have similar views than you, and this
> explanation brought in Clifford algebra, not my
> correction of Virgil's misconception.
Well, Pertti, I guess I'm just an idiot - you'll
have to spell it out more plainly for me. You
used your knowledge of people in the field of
Clifford algebra research as a defense against having
to be polite to the people in this thread. That sure
seems to me as if you are implying that the subject
being discussed in this thread is indeed Clifford
algebra. If it was not, then what exactly did you mean?
> Now you
> have repeatedly presented views on my research
> topic, Clifford algebras, which are not accurate,
> or are misplaced. Would I be rude, if I would
> correct your misplaced views, in detail? Or
> would I be unhelpful toward you, if I let you
> hold on your views?
I would hope and expect you to clear up any and
all misplaced views. Why wouldn't I?
--
Randy Yates
DSP Engineer
Ericsson / Research Triangle Park, NC, USA
qus...@rtp.ericsson.se, 919-472-1124
.
Jerry Avins
WRONG! ;-) In grade school, I asked the teacher how the long division
procedure worked, and she didn't understand that it was a legitimate
question. "Just multiply it out and you'll see that it does", as if that
were an explanation. I devised my own clumsy method, which after
successive refinement ended up the same as what she had taught me. The
only difference was that I was the only one in the room who understood
the reasoning behind it. The term before, with a different teacher, I
couldn't learn the multiplication tables (I now recognize a learning
disability - then I was called lazy), so I used a method that required
only halving, doubling, and adding. The only way I could explain it then
was that, when converted to binary, it was the same procedure as the
standard one. To explain my method to the teacher, I had first to
introduce her to the concept of number bases other than ten. It was time
consuming, but interesting for both of us. That was around 1942; what
were you doing then?
Jerry Avins
Your process of deduction leaves much to be desired, and must lead you
to frequent error. From what do you conclude that we failed to find the
counterexample? The truth is that I, for one, have not thought about it
at all.
Jerry
--
Never argue with a pig. You'll both get dirty, but the pig likes it.
--------------------------------------------------------------------
Pertti Lounesto
> Your process of deduction leaves much to be desired,
> and must lead you to frequent error.
but fails to point out a single error in my mathematics,
as presented in wb-pages:
http://www.hit.fi/~lounesto/counterexamples.htm
http://www.hit.fi/~lounesto/Robin.Chapman
>>Doug & Jerry do not understand why I/(I+B), B in
>> SO(n), is interesting, but wanted to write follow-ups
>> on that.
>
> WRONG! ;-) In grade school, I asked the teacher
> how the long division.
WRONG! Long division is not of interest here, for
B in SO(n), where has no eigenvalues of -1. The
interest is in proving this (in an elementary way) and
trying to carry the elementary proof to the two-fold
covering group of SO(n).
Pertti Lounesto
In my responce to Virgil's posting, claiming non-
existence of a general formula relating inv(A+B) to
A,B,inv(A),inv(B), I corrected Virgil's misconception
by the counterexample (here without mispronts)
inv(A+B) = inv(A)-inv(A) B inv(A)+-...,
which converges with respect to a norm defined by
a convex, symmetric, expelling and absorbing set.
Your first assumption about Clifford algebras entering
at this point is false, and therefore all your conclusions
drawn from your first initial assumptions are invalid,
and not worthy of comment, irrespective of what
further assumptions you make.
> > I would never imagine Virgil to
> > know anything about Clifford algebras. You
> > intervented into the discussion by inserting a
> > quote on me "relishing in shouting wrong" and
> > then explained me being rude.
>
> Excuse me? Intervened? As if *my* comments were
> not allowed, while those of any other general
> poster are?
Exactly. Your comments were a fallacy, because
you appealed for the opinion of others, by quoting
them. Thus, instead of attacking on my arguments,
you reasoned against my person by pointing out that
other posters have made negative comments about me.
Such commentary is not valid argumentation, but fallacy,
see http://members.icanect.net/~zardoz/fallacies.htm.
> > I responded to
> > you by explaining why in general posters in
> > sci.math have similar views than you, and this
> > explanation brought in Clifford algebra, not my
> > correction of Virgil's misconception.
>
> Well, Pertti, I guess I'm just an idiot - you'll
> have to spell it out more plainly for me. You
> used your knowledge of people in the field of
> Clifford algebra research as a defense against having
> to be polite to the people in this thread.
This is incorrect. In your first response to my
postings, you had cut out the part, where I wrote
about Clifford algebras. Thus, you first comment
was a response to something else than my writing
on Clifford algebras. This can be seen from your
comment
> [you] *presume* a person is like this when knowing
> relatively little about them is, in my opinion, rude.
which shows that you were talking about my response
to Virgil (about whom I know relativily little) and not
about the (cut-out) academician on Clifford algebra
(whom I knew very well personally, and whose relation
with me you cannot possible know; in fact he is a
student of mine -- in the sense that his main results
he reached by my teachings).
> That sure
> seems to me as if you are implying that the subject
> being discussed in this thread is indeed Clifford
> algebra. If it was not, then what exactly did you mean?
No. As you cut out the Clifford algebra part, in your
first response, you are not entitled to draw such a
conclusion. My correction of Virgil's misconception
was not based on Clifford algebra, and you admitted
that you understood that I responded to Virgil, in your
response when you claimed that I *presume* a person
is ... when knowing relatively little (of Virgil).
> > Now you
> > have repeatedly presented views on my research
> > topic, Clifford algebras, which are not accurate,
> > or are misplaced. Would I be rude, if I would
> > correct your misplaced views, in detail? Or
> > would I be unhelpful toward you, if I let you
> > hold on your views?
>
> I would hope and expect you to clear up any and
> all misplaced views. Why wouldn't I?
That would require that I teach you Clifford algebra,
in the full. For this, read the book on Clifford algebras
and their uses in geometry, in particular rotations,
http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521599164
Clifford algebra is a much wider topic than you insinuate.
Open the thread "Unitary transformation" and see how
I use Clifford algebra, in particular Lipschitz' results, to
enhance and overcome, in an elegant and efficient way,
classical results of Jordan, Dieudonne, Davis, Kahan, etc.
Learn the power and simplicity of Clifford algebras, and
then go on with your commentary, better informed.
Randy Yates
> [...]
> In my responce to Virgil's posting, claiming non-
Mr. Lounesto,
I give up. I have tried in good faith to communicate
with you. It appears that communicating with you takes
so much time and energy that it would absorb other
more fruitful endeavors. I am therefore terminating
my involvement in this thread.
Clay S. Turner
Jerry Avins wrote:
>
>
>
> I don't know what you should _say_, but it seems to me that you should
> _think_ that something about the way you express yourself makes people
> want to pick on you. Perhaps you can do something to change that; if
> not, you might enjoy a private correspondence with E. Robert Tisdale
> <ed...@netwood.net>.
Hello Jerry et al.,
I may be a bit juvenile here, but the similar actions of these two begs
the question of which one has the smaller penis? Maybe they both suffer
from microphallus and this explains their "better than everyone else"
attitudes. I pity them both.
Clay
Peter J. Kootsookos
| I may be a bit juvenile here, but the similar actions of these two begs
| the question of which one has the smaller penis?
That's a little below the belt, isn't it?
:-|
--
Peter J. Kootsookos
http://www.clubi.ie/PeterK
Jerry Avins
Read carefully: I do not claim that you are wrong; rather, I claim that
you are stupid. Let me be clear that I confine the charge of stupidity
to the faculty of social savvy; that is the only part of your nature
that is clearly delineated in your posts.
This discussion is not about (nor was it ever about) Clifford algebras.
It has not been about matrix inverses for many exchanges now, either. It
is about the way you present yourself to strangers, and the unwarranted
and usually erroneous assumptions you make about them. I hope you will
have learned something from it, but I doubt have doubts.
Jerry
--
Engineering is the art of making what you want from things you can get.
-----------------------------------------------------------------------
Pertti Lounesto wrote:
>
> Randy Yates wrote:
>
...
> > >
> > > This is false.
> >
> > *What* is false? I made two assertions above. To which
> > are you responding? The second? Both? As a mathematician,
> > I expect you to be clear. The use of such an imprecise
> > definite article in this context is negligent.
>
> In my responce to Virgil's posting, claiming non-
> existence of a general formula relating inv(A+B) to
> A,B,inv(A),inv(B), I corrected Virgil's misconception
> by the counterexample (here without mispronts)
>
> inv(A+B) = inv(A)-inv(A) B inv(A)+-...,
>
...
> > > I responded to
> > > you by explaining why in general posters in
> > > sci.math have similar views than you, and this
> > > explanation brought in Clifford algebra, not my
> > > correction of Virgil's misconception.
> >
> > Well, Pertti, I guess I'm just an idiot - you'll
> > have to spell it out more plainly for me. You
> > used your knowledge of people in the field of
> > Clifford algebra research as a defense against having
> > to be polite to the people in this thread.
>
> This is incorrect. In your first response to my
> postings, you had cut out the part, where I wrote
> about Clifford algebras. Thus, you first comment
> was a response to something else than my writing
> on Clifford algebras. This can be seen from your
> comment
>
> ...
Jerry Avins
That was not my intention, and I apologize for invading his privacy.
This is posted here because he asked me not to email him again, and I
respect his wishes.
Jerry
I wrote:
>
> Pertti,
>
> Read carefully: I do not claim that you are wrong; rather, I claim that
> you are stupid. Let me be clear that I confine the charge of stupidity
> to the faculty of social savvy; that is the only part of your nature
> that is clearly delineated in your posts.
>
> This discussion is not about (nor was it ever about) Clifford algebras.
> It has not been about matrix inverses for many exchanges now, either. It
> is about the way you present yourself to strangers, and the unwarranted
> and usually erroneous assumptions you make about them. I hope you will
> have learned something from it, but I doubt have doubts.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> -----------------------------------------------------------------------
> Pertti Lounesto wrote:
> >
> > Randy Yates wrote:
> >
> ...
> > > >
> > > > This is false.
> > >
> > > *What* is false? I made two assertions above. To which
> > > are you responding? The second? Both? As a mathematician,
> > > I expect you to be clear. The use of such an imprecise
> > > definite article in this context is negligent.
> >
> > In my responce to Virgil's posting, claiming non-
> > existence of a general formula relating inv(A+B) to
> > A,B,inv(A),inv(B), I corrected Virgil's misconception
> > by the counterexample (here without mispronts)
> >
> > inv(A+B) = inv(A)-inv(A) B inv(A)+-...,
> >
> ...
>
> > > > I responded to
> > > > you by explaining why in general posters in
> > > > sci.math have similar views than you, and this
> > > > explanation brought in Clifford algebra, not my
> > > > correction of Virgil's misconception.
> > >
> > > Well, Pertti, I guess I'm just an idiot - you'll
> > > have to spell it out more plainly for me. You
> > > used your knowledge of people in the field of
> > > Clifford algebra research as a defense against having
> > > to be polite to the people in this thread.
> >
> > This is incorrect. In your first response to my
> > postings, you had cut out the part, where I wrote
> > about Clifford algebras. Thus, you first comment
> > was a response to something else than my writing
> > on Clifford algebras. This can be seen from your
> > comment
> >
> > ...
Randy Yates
>
> Clay S. Turner <cstu...@peachnet.campuscwix.net> wrote
>
> | I may be a bit juvenile here, but the similar actions of these two begs
> | the question of which one has the smaller penis?
>
> That's a little below the belt, isn't it?
>
> :-|
In my case, it's below the knee...
--
% Randy Yates % "...the answer lies within your soul
%% DIGITAL SOUND LABS % 'cause no one knows which side
%%% Digital Audio Sig. Proc. % the coin will fall."
%%%% <ya...@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO
http://207.87.184.178/index.htm
Pertti Lounesto
> "Peter J. Kootsookos" wrote:
> >
> > Clay S. Turner <cstu...@peachnet.campuscwix.net> wrote
> >
> > | I may be a bit juvenile here, but the similar actions of these two begs
> > | the question of which one has the smaller penis?
> >
> > That's a little below the belt, isn't it?
> >
> > :-|
>
> In my case, it's below the knee...
Does that mean that you are impotent?
David C. Ullrich
Pertti Lounesto wrote:
> Randy Yates wrote:
>
> > The original question involved only the vector space
> > of matrices over the complex field.
>
> I corrected misconception of a responder, Virgil,
> in the setting of matrices over the complex field.
Actually you said "Wrong" and then said something
ridiculous which you _thought_ was a correction.
>
> > This is presumably much
> > more limited in scope then Clifford algebras
> > and also probably much more widely studied.
>
> Concerning posters commenting on my math, you
> presented views on my evaluation of such posters.
> I explained my views, and this explanation brought
> in my mathematics, Clifford algebras.
David C. Ullrich
Pertti Lounesto wrote:
> [...]
>
> In my responce to Virgil's posting, claiming non-
> existence of a general formula relating inv(A+B) to
> A,B,inv(A),inv(B), I corrected Virgil's misconception
> by the counterexample (here without mispronts)
>
> inv(A+B) = inv(A)-inv(A) B inv(A)+-...,
>
> which converges with respect to a norm defined by
> a convex, symmetric, expelling and absorbing set.
What??? Presumably you mean that there is such
a norm with respect to which this series converges
for any A and B, or even that for any A and B there
is such a norm with respect to which this converges?
That's ridiculous.
In your original response it looked like you thought
every series converged, which was sort of stupid because
people had pointed out to you before that not every
series converged. You said that was a slip. Now you've
had time to think it over and you come up with this?
Incredible.
Johannes H Andersen
"David C. Ullrich" wrote:
>
> Pertti Lounesto wrote:
>
> > [...]
> >
> > In my responce to Virgil's posting, claiming non-
> > existence of a general formula relating inv(A+B) to
> > A,B,inv(A),inv(B), I corrected Virgil's misconception
> > by the counterexample (here without mispronts)
> >
> > inv(A+B) = inv(A)-inv(A) B inv(A)+-...,
> >
> > which converges with respect to a norm defined by
> > a convex, symmetric, expelling and absorbing set.
>
> What??? Presumably you mean that there is such
> a norm with respect to which this series converges
> for any A and B, or even that for any A and B there
> is such a norm with respect to which this converges?
> That's ridiculous.
> In your original response it looked like you thought
> every series converged, which was sort of stupid because
> people had pointed out to you before that not every
> series converged. You said that was a slip. Now you've
> had time to think it over and you come up with this?
> Incredible.
>
Yes, convergence or divergence are indepent of which matrix
norm you choose. Say we have two norms f() and g() which
satisfies the usual norm criteria including the triangle
condition. Since norms are linear with respect to scalars,
then it is always possible to find numbers a,b such that:
f() =< a g() and
g() =< b f()
Johannes
> >+...
Virgil
>> Pertti Lounesto wrote:
>>
>> > [...]
>> >
>> > In my responce to Virgil's posting, claiming non-
>> > existence of a general formula relating inv(A+B) to
>> > A,B,inv(A),inv(B), I corrected Virgil's misconception
>> > by the counterexample (here without mispronts)
>> >
>> > inv(A+B) = inv(A)-inv(A) B inv(A)+-...,
>> >
>> > which converges with respect to a norm defined by
>> > a convex, symmetric, expelling and absorbing set.
I think it cute of Pertti to include a "mispront" in his "responce"
statement guaranteed to be without misprints, but not without
misspellings.
If I had known Pertti was likely to get into the act, I would have
phrased my statement more carefully. There STILL is no formula
guaranteed to give an exact result in a finite number of steps, which I
believe to have been the result requested by the original poster. If my
belief was incorrect, my apologies to the original poster.
In any case, to the rest of you, let it die.
--
Virgil
vm...@frii.com
Pertti Lounesto
> >> Pertti Lounesto wrote:
> >>
> >> > [...]
> >> >
> >> > In my responce to Virgil's posting, claiming non-
> >> > existence of a general formula relating inv(A+B) to
> >> > A,B,inv(A),inv(B), I corrected Virgil's misconception
> >> > by the counterexample (here without mispronts)
> >> >
> >> > inv(A+B) = inv(A)-inv(A) B inv(A)+-...,
> >> >
> >> > which converges with respect to a norm defined by
> >> > a convex, symmetric, expelling and absorbing set.
>
> I think it cute of Pertti to include a "mispront" in his "responce"
> statement guaranteed to be without misprints, but not without
> misspellings.
>
> If I had known Pertti was likely to get into the act, I would have
> phrased my statement more carefully. There STILL is no formula
> guaranteed to give an exact result in a finite number of steps, which I
> believe to have been the result requested by the original poster. If my
> belief was incorrect, my apologies to the original poster.
>
> In any case, to the rest of you, let it die.
So, according to you, my construction of a counterexample,
to the wording of your response to the original poster, was
not useful to you. Maybe all the dull rich responses to my
counterexample are more useful postings, in general? As I
am useless as a corrector of your misconceptions, maybe
it is a proper act of you to join the army of all those dullrich
posters, whose misconceptions I have previously corrected?
See http://www.hit.fi/~lounesto/dullrich.
H. Paul Jacobson
> Virgil wrote:
> > If I had known Pertti was likely to get into the act, I would have
> > phrased my statement more carefully. There STILL is no formula
> > guaranteed to give an exact result in a finite number of steps, which I
> > believe to have been the result requested by the original poster. If my
> > belief was incorrect, my apologies to the original poster.
Considering that this thread was sent to the MATLAB newsgroup (as well as
sci.math), I'd guess that the original poster wanted something practical,
not just a pure 'existence or non existence' argument. Numerical analysis
abounds with iterative methods for finding matrix inverses. As one who
has followed this argument from the applied side I'm of the opinion that
Pertti's solution (as amended by others) is the most useful one. The
other posts have also been revealing - showing the mathematicians are as
human as the rest of us :-)
Paul Jacobson (geophysics)
p.s. I've had to do some large matrix inversions in MATLAB as part of
finite element solutions. So far I've focused on building the large
sparse matricies, and let MATLAB worry about the most efficient way of
doing the inversion.
David C. Ullrich
> [...]
>
> So, according to you, my construction of a counterexample,
> to the wording of your response to the original poster, was
> not useful to you.
What the heck are you babbling about? Your "counterexample"
was simply _wrong_. It contained the same "math error" that
I pointed out to you some years ago: not every series converges.
This is something you're supposed to know after you take
calculus - the idea that it has to be explained to you twice
is sort of, well, words fail me.
You said it was a slip. Now the other day you post _more_
absolute nonsense about how the series converges with respect
to some other norm. _Many_ people explain to you that not
every series converges, and you think you change that by adding
words you read in some functional analysis book. And you're
still talking about your "counterexample" here? Incredible.
> Maybe all the dull rich responses to my
> counterexample are more useful postings, in general?
WHAT counterexample?
Really. You keep asking why people evaluate your mathematics
without looking at it. But you keep boasting about your ignorance
of first-year graduate student topics, and you keep _repeating_
the same error in the same thread, after it's been explained to you.
Are all of your famous counterexamples as utterly bogus as
this one?
> As I
> am useless as a corrector of your misconceptions, maybe
> it is a proper act of you to join the army of all those dullrich
> posters, whose misconceptions I have previously corrected?
>
> See http://www.hit.fi/~lounesto/dullrich.
Yes, we should see that if we're interested in misquotation
and misrepresentation regarding trivia.
David C. Ullrich
> "David C. Ullrich" wrote:
> >
> > Pertti Lounesto wrote:
> >
> > > [...]
> > >
> > > In my responce to Virgil's posting, claiming non-
> > > existence of a general formula relating inv(A+B) to
> > > A,B,inv(A),inv(B), I corrected Virgil's misconception
> > > by the counterexample (here without mispronts)
> > >
> > > inv(A+B) = inv(A)-inv(A) B inv(A)+-...,
> > >
> > > which converges with respect to a norm defined by
> > > a convex, symmetric, expelling and absorbing set.
> >
> > What??? Presumably you mean that there is such
> > a norm with respect to which this series converges
> > for any A and B, or even that for any A and B there
> > is such a norm with respect to which this converges?
> > That's ridiculous.
> > In your original response it looked like you thought
> > every series converged, which was sort of stupid because
> > people had pointed out to you before that not every
> > series converged. You said that was a slip. Now you've
> > had time to think it over and you come up with this?
> > Incredible.
> >
>
> Yes, convergence or divergence are indepent of which matrix
> norm you choose. Say we have two norms f() and g() which
> satisfies the usual norm criteria including the triangle
> condition. Since norms are linear with respect to scalars,
> then it is always possible to find numbers a,b such that:
>
> f() =< a g() and
> g() =< b f()
You know that and I know that. Anyone who has a clue regarding
what the word "norm" has to do with the phrase "finite dimensional"
knows that. But if you're a child prodigy and you're proud of your
ignorance of almost any area of mathematics one could name then
it can be hard to get these things straight.
I almost wonder whether he actually had something in mind.
Heh-heh: I bet someone told him that
(i) If A has norm less than 1 then the series 1 + A + A^2... converges,
and someone else told him that
(ii) For any A there is a norm n such that n(A) < 1.
Both are true statements, in the proper context. If your specialty
is taking things out of context then you might conclude from
(i) and (ii) that
(iii) For any A there is a norm n with respect to which
1 + A + ... converges.
(For lurkers: No, (iii) actually does not follow from (i)
and (ii). Because the norm in (i) is a particular norm, not
just any norm. Well, lots of norms work in (i) - any
"operator norm", or more generally any norm with
(iv) ||AB|| <= ||A||*||B||.
But if you take a norm satisfying (iv) and divide it
by 2 it may well not satisfy (iv) any more...)
It's really more hilarious than usual. Making the
same mistake once every few years he can claim all
sorts of things. But when people explain to him that
not every series converges and he comes up with this
gibberish a few days later it's truly remarkable. I
mean people explain the series simply does not
converge and instead of thinking about why not
he looks for magic words, like saying "convex,
symmetric, expelling and absorbing set" is going
to change the divergence. We need to add
"calculus 101" to the list "axiom of choice,
quadratic reciprocity".
> Johannes
>
> > >+...
Johannes H Andersen
"David C. Ullrich" wrote:
>
> Johannes H Andersen wrote:
>
> > "David C. Ullrich" wrote:
> > >
> > > Pertti Lounesto wrote:
> > >
> > > > [...]
> > > >
> > > > In my responce to Virgil's posting, claiming non-
> > > > existence of a general formula relating inv(A+B) to
> > > > A,B,inv(A),inv(B), I corrected Virgil's misconception
> > > > by the counterexample (here without mispronts)
> > > >
> > > > inv(A+B) = inv(A)-inv(A) B inv(A)+-...,
> > > >
> > > > which converges with respect to a norm defined by
> > > > a convex, symmetric, expelling and absorbing set.
> > >
>+.........
This is my very last word in this thread - and I mean it - really.
Sorry for having stated the obvious, but I think that sci.math
should be a place for everybody with a genuine interest in math,
not just frontline research. After all there are many mathematicians
out there who are not in a Math department, but are using math
in all sorts of inspired ways for solving actual real life
problems. I count myself in this category.
Amazingly, it was last saturday he invaded this thread and the usual
destructive pattern has emerged. Looks like Clifford algebra is
interesting stuff though. Sooner or later I will read up on it
and would not mind this person to hand something down to in a
form which is suitable for the non-specialist. But will he ever
grow up.
Johannes
Pertti Lounesto
> "operator norm", or more generally any norm with
>
> (iv) ||AB|| <= ||A||*||B||.
>
> But if you take a norm satisfying (iv) and divide it
> by 2 it may well not satisfy (iv) any more...)
>
> It's really more hilarious than usual. Making the
> same mistake once every few years he can claim all
> sorts of things.
The fact that I did not mention convergence was
not a mistake; I assumed that informed readers can
fill in trivial tacit assumptions, like convergence.
Evidently, I was mistaken with respect to you as
an "informed reader". Before going on with your
claims about me not knowing about convergence,
norms and rescaling of (iv), I guide you to read
P. Lounesto: Counterexamples in Clifford algebras,
Advances in Applied Clifford Algebras 6 (1996), 69-104,
http://www.clifford.org/~clf-alg/journals/jadvclfa.html.
There I discuss about norms on Clifford algebras on
definite quadratic spaces, namely Cl_n on R^n and
Cl_{0,n} on R^{0,n}. I point out that Constales 1989
and Habetha 1985 know that
|uv| <= 2^(n/2)|u||v|
and admit that 2^(n/2) is not optimal, but refer to a
better estimate in case Cl_{0,n}, namely
H_{0,n} = sqrt(2^(n-1)(1+2^((1-n)/2)cos((n+1)pi/4))).
I show that Constales and Habetha did not give the
best estimate, which is
n K_{0,n} K_n
==============
1 1 sqrt(2)
2 1 sqrt(2)
3 sqrt(2) sqrt(2)
4 sqrt(2) sqrt(2)
5 2 2
6 2sqrt(2) 2
7 4 2sqrt(2)
8 4 4
and which continue with recursions K_{0,n+8} = 4K_{0,n}
and K_{n+8} = 4K_n. According to your I managed to find
out best estimates of the coefficients in |uv| <= K_n|u||v|
and |uv| <= K_{0,n}|u||v| and managed to enhance works of
such renowned researchers as Constales and Habetha, without
knowing anything about norms/convergence? You might
also want to read my joint paper in spinor norms:
G.N. Hile, P. Lounesto: Inequalities for spinor norms in
Clifford algebras, in A. Trautman, G. Furlan: Spinors in
Physics and Geometry (Trieste 1986), 1988.
But, of course, in a joint paper, the parts of norms are
written by my co-author. For those interested in dull
rich postings and mistakes of D. Ullrich , point your
browser to
Pertti Lounesto
> "David C. Ullrich" wrote:
> > Lynn Killingbeck wrote:
> > > "David C. Ullrich" wrote:
> > > > Pertti Lounesto intended to write:
> > > >
> > > > > [...]
> > > > >
> > > > > Virgil is wrong when he claims that there does not
> > > > > exist a general formula relating inv(A+B) to
> > > > > A,B,inv(A),inv(B), since
> > > > >
> > > > > f(A,B) = inv(A+B) = inv(A)-inv(A) B inv(A)+-...
> > > > >
> > > > > is holds for some (A,B) in a convex, symmetric,
> > > > > expelling and absorbing domain around (0,0).
Lynn Killingbeck wrote (in line with Ullrich and Andersen):
> There is the constraint about existence of A, B, A', and B'.
> Even after fixing the sign mistake, the series clearly fails
> for A=B=1. But, others have already beat down the blunder
> about convergence considerations. A=1, B=2 fails
> horribly, because of failure to consider convergence.
Thus, when Lounesto assumes that posters of sci.math have
enough general knowledge of mathematics, that they can fill in
tacit assumptions of trivialities (in this case about convergence),
Lounesto's "blunder" "horribly" "fails".
On Mar 19, Killingbeck errs (Ullrich & Andersen fail to detect error):
> My own intuition is that, if there is some norm N() such that
> N(B)<N(A), then the technique converges. If the strict
> inequality is the other direction, interchange A<->B. If N(A)=N(B),
> I give up. All by analogy to the expansion of 1/(1+x)=1-x+x^2-x^3+-...
> converging for |x|<1.
Wrong. Counterexample A = [2 0,0 1/2] and B = I. The spectral
radius of B*inv(A) is 2, and interchanging the roles of A and B does
not change the situation, that is, both f(A,B) and f(B,A) diverge.
The inability of David Ullrich and Johannes Andersen to detect
errors, when the errors are essential misconceptions, instead of
delibarate omissions made to make the presentation short, shows
that Lounesto's "blunder" is that he "horribly" "fails" to evaluate
the math-abilities of sci.math posters realistically, while there is
no bottom.
Lynn Killingbeck, David Ullrich and Johannes Andersen keep
silent about the posting of Paul Jacobson:
On 25 Mar, 2000, Paul Jacobson wrote:
> As one who has followed this argument from the applied
> side I'm of the opinion that Pertti's solution (as amended by
> others) is the most useful one.
It is easy to predict the group-behaviour of the dullrich-group:
Jacobson is bad, Virgil is good, Killingbeck is good, etc. There
is no end.
David C. Ullrich
> "David C. Ullrich" wrote:
>
> > "operator norm", or more generally any norm with
> >
> > (iv) ||AB|| <= ||A||*||B||.
> >
> > But if you take a norm satisfying (iv) and divide it
> > by 2 it may well not satisfy (iv) any more...)
> >
> > It's really more hilarious than usual. Making the
> > same mistake once every few years he can claim all
> > sorts of things.
>
> The fact that I did not mention convergence was
> not a mistake; I assumed that informed readers can
> fill in trivial tacit assumptions, like convergence.
This is nonsense. You began with a "couterexample"
that involved a series that simply did not converge. The
problem was not that you did not _mention_ convergence,
the problem was that the series does _not_ converge,
making your "counterexample" simply wrong.
Anyone can make a mistake (some people can even
admit it when it happens). This didn't get hilarious
until that post a few days ago, where (after the non-
convergence had been pointed out) you _said_
that the series _did_ converge in some norm!
In that last post you did not ignore convergence,
you _said_ the series _did_ converge in some norm.
Which is simply not so - for typical A and B it
does not converge in _any_ norm. (Suggesting
that it might converge in one norm but not in
another reveals some serious gaps in your
cognitive structures.)
> Evidently, I was mistaken with respect to you as
> an "informed reader". Before going on with your
> claims about me not knowing about convergence,
> norms and rescaling of (iv), I guide you to read
If you know so much about norms then why
did you say the series converged in some norm?
The way you're behaving right now really does
not do much for your credibility, you know. You
always complain about people being unable to
invalidate your counterexamples, as though
anyone cared. Here you've been found making
elementary math errors, then _repeating_ the
_same_ error a few days later, thinking that
adding a few words from functional analysis
would make a divergent series converge. And
all you can do is go on about how much you
know about norms?
Leads one to suspect that when a person
_does_ "invlaidate" one of your counterexamples
you simply ignore it, then go back to claiming
it's never been done. I bet that happens a lot, eh?
David C. Ullrich
> Johannes H Andersen wrote:
>
> > "David C. Ullrich" wrote:
> > > Lynn Killingbeck wrote:
> > > > "David C. Ullrich" wrote:
> > > > > Pertti Lounesto intended to write:
> > > > >
> > > > > > [...]
> > > > > >
> > > > > > Virgil is wrong when he claims that there does not
> > > > > > exist a general formula relating inv(A+B) to
> > > > > > A,B,inv(A),inv(B), since
> > > > > >
> > > > > > f(A,B) = inv(A+B) = inv(A)-inv(A) B inv(A)+-...
> > > > > >
> > > > > > is holds for some (A,B) in a convex, symmetric,
> > > > > > expelling and absorbing domain around (0,0).
>
> Lynn Killingbeck wrote (in line with Ullrich and Andersen):
>
> > There is the constraint about existence of A, B, A', and B'.
> > Even after fixing the sign mistake, the series clearly fails
> > for A=B=1. But, others have already beat down the blunder
> > about convergence considerations. A=1, B=2 fails
> > horribly, because of failure to consider convergence.
>
> Thus, when Lounesto assumes that posters of sci.math have
> enough general knowledge of mathematics, that they can fill in
> tacit assumptions of trivialities (in this case about convergence),
> Lounesto's "blunder" "horribly" "fails".
>
> On Mar 19, Killingbeck errs (Ullrich & Andersen fail to detect error):
Many people have said many false things in this thread. Not everyone
who's said something false is the sort of pompous ass who goes on
about how he's the greatest falsifier of theorems in history, or the
sort of pompous ass who goes on about how he's _proud_ of his
ignorance of the axiom of choice and quadratic recoprocity.
> > My own intuition is that, if there is some norm N() such that
> > N(B)<N(A), then the technique converges. If the strict
> > inequality is the other direction, interchange A<->B. If N(A)=N(B),
> > I give up. All by analogy to the expansion of 1/(1+x)=1-x+x^2-x^3+-...
> > converging for |x|<1.
>
> Wrong.
He didn't even say it was so, he said that was his intuition.
You're the greatest [several things] in history, and you're blaming
your blunder on some _speculations_ of this Killingbeck guy?
Why, he's not even smart enough to insist that anything he
doesn't know is worthless!
> Counterexample A = [2 0,0 1/2] and B = I. The spectral
> radius of B*inv(A) is 2, and interchanging the roles of A and B does
> not change the situation, that is, both f(A,B) and f(B,A) diverge.
>
> The inability of David Ullrich and Johannes Andersen to detect
> errors, when the errors are essential misconceptions, instead of
> delibarate omissions made to make the presentation short,
In the second post - the one I keep calling "hilarious", the one
where you did not omit questions of convergence, the one where
you said the series _does_ converge in some norm. In that second
post you delibarately omitted the word "not" to make the
presentation short? Got it.
What an ass.
> shows
> that Lounesto's "blunder" is that he "horribly" "fails" to evaluate
> the math-abilities of sci.math posters realistically, while there is
> no bottom.
>
> Lynn Killingbeck, David Ullrich and Johannes Andersen keep
> silent about the posting of Paul Jacobson:
That was yesterday - I just got here.
David C. Ullrich
prizes for most useful solution. Go back to the top: The same
day I saw Pertti's solution I saw two other people give
_correct_ statements of exactly the same solution! The fact
that their solutions were actually 100% correct means they
did not generate as much noise. I would think that the prize
for most useful solution should go to the guys who actually
got it right, unless you can explain somehow how Pertti's
incorrect version was more useful than their correct ones.
(I know Pertti's going to jump in explaining exactly that.
What an ass.)
"H. Paul Jacobson" wrote:
> On Sat, 25 Mar 2000, Pertti Lounesto wrote:
>
> > Virgil wrote:
> > > If I had known Pertti was likely to get into the act, I would have
> > > phrased my statement more carefully. There STILL is no formula
> > > guaranteed to give an exact result in a finite number of steps, which I
> > > believe to have been the result requested by the original poster. If my
> > > belief was incorrect, my apologies to the original poster.
>
> Considering that this thread was sent to the MATLAB newsgroup (as well as
> sci.math), I'd guess that the original poster wanted something practical,
> not just a pure 'existence or non existence' argument. Numerical analysis
> abounds with iterative methods for finding matrix inverses. As one who
> has followed this argument from the applied side I'm of the opinion that
> Pertti's solution (as amended by others) is the most useful one. The
> other posts have also been revealing - showing the mathematicians are as
> human as the rest of us :-)
And you should review the history of sci.math for the last few years
before deciding what the other posts show.
Jeff Stuart
Let us be thankful that Pertti spends his empty
hours writing whiney letters to newsgroups about
how underappreciated his command of Clifford
algebras is and about how people just don't
understand that he is the world's greatest master
of counterexamples (which he must be since he
tells us he is). It could be much worse, he could be
more like the imfamous social misfit and mathematician,
Ted Kazinski, who spent his idle hours whittling bomb
triggers in a primitive shack up in Montana. It's
easy to speculate that both share the same personality
flaws - an inability to have comfortable interpersonal
contact with others coupled with an enormous conflict
over self-worth and self-worthlessness. Fortunately,
Pertti does not seem to possess the same degree of
violent tendancies since he limits himself to insulting
the intelligence of everyone who crosses him, rather
than mailing them bombs.
J. Stuart
David C. Ullrich wrote in message <38DE769A...@math.okstate.edu>...
Erik Max Francis
> David, have you considered seeking for professional help?
What an ironic thing for you to say.
--
Erik Max Francis | email m...@alcyone.com | icq 16063900
Alcyone Systems | web http://www.alcyone.com/max/ | q3a Product
San Jose, CA | languages en, eo | icbm 37 20 07 N 121 53 38 W
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__
/ \ If a thing is worth doing, then it is worth doing badly.
\__/ G.K. Chesterton
Erik Max Francis
> Why don't you two morons try find the complete solution
> to the problem of a true mathematician, Zdislav Kovarik:
> Find all rotations, U, of R^4 sending a plane, A, to another, B.
Uh oh! Lounesto's about to burst. Everybody stand back and watch the
fun.
--
Erik Max Francis | email m...@alcyone.com | icq 16063900
Alcyone Systems | web http://www.alcyone.com/max/ | q3a Product
San Jose, CA | languages en, eo | icbm 37 20 07 N 121 53 38 W
USA | 968.292 Ms p.L. | 280 days left | &tSftDotIotE
__
/ \ I love Mickey Mouse more than any woman I've ever known.
\__/ Walt Disney
Doug Norris
>Fortunately,
>Pertti does not seem to possess the same degree of
>violent tendancies since he limits himself to insulting
>the intelligence of everyone who crosses him, rather
>than mailing them bombs.
So far.
Doug
Pertti Lounesto
You were the first one to respond to my solution of Mar 18,
2000, the one-line posting of
> inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
which containded a sign-error and which took for granted
that sci.math posters can figure out the proper domain of
convergence by themselves. You responded twice, but
did not manage to notice the sign-error. Now you want to
give credit to those two posters, who corrected my trivial
sign error. Should you not rather give credit only to the
first corrector, Johannes Andersen, who wrote
> > inv(A+B) = inv(A)+inv(A) B inv(A)+inv(A) B inv(A) B inv(A)+...
>
> Do you mean:
>
> inv(A+B) = inv(A)+inv(A)(-B) inv(A)+inv(A)(-B) inv(A) (-B) inv(A)+...
>
> Converges if the spectral radius of inv(A)B is less than 1
and who also completed my solution by proper convergence
considerations?
You dwell into the trivial matter of convergence, and claimed
that I would not have known that the series does not
convergence for all A and B. Although you obsessed on
convergence, you refrained from correcting Lynn Killingbeck's
misconception about convergence,
> My own intuition is that, if there is some norm N() such that
> N(B)<N(A), then the technique converges. If the strict
> inequality is the other direction, interchange A<->B. If N(A)=N(B),
> I give up. All by analogy to the expansion of 1/(1+x)=1-x+x^2-x^3+-...
> converging for |x|<1.
which can be shown wrong by the counterexample B = I and
A = [2 0,0 1/2], which does not allow interchange A <-> B.
You did not correct Zdislav Kovarik, who incorrectly claimed
that there exist no expression for inv(A+B) in terms of A, B,
inv(A) and inv(B). You did not correct Virgil, who made the
same bogus claim.
You did not correct any of those, who considered the series
1/(1+x) = 1-x+x^2-x^3+-... and claimed that no matrix analogy
exists for I/(A+B).
And you object somebody, who credited me for coming as the
first one, who related I/(A+B) to A, B, inv(A) and inv(B). And, ...
David, have you considered seeking for professional help for
your obsession on relishing about my trivial sign error and
omission of trivial tacit assumtions? And your obsession of
closing your eyes of misconceptions of other posters?