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Bug on the HP49 with eigenvectors

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bk

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Jan 28, 2001, 6:21:05 PM1/28/01
to
i tried to find the eigenvalues and eigenvectors for the following 4*4
matrix (with complex Elements...)
[-3 1 0 0]
[-1 -3 0 0]
[ 0 0 0 1]
[ 0 0 0 3]

i find out: eigenvalues are: (-i, i, 3, 3) which are correct.
trying to find out the eigenvectors, the calc tels me: [EGV Error: Matrix
not diagonalizable]. But [0 0 1 0] , [1 i 0 0] and [1 -i 0 0] are
eigenvectors...
I use Version 1,19-5


Virgil

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Jan 29, 2001, 1:52:04 AM1/29/01
to
In article <9529hc$1bp$1...@infosun2.rus.uni-stuttgart.de>, "bk"
<bil...@studserv.uni-stuttgart.de> wrote:

The 4x4 matrix shown above has no complex elements.
Its eigenvalue set is { 0,3,-3+i,-3-i}
Its eigenvector matrix (columns are eigen vectors) is

[[ 0 0 1 -i ]
[ 0 0 -i 1 ]
[ 1 1 0 0 ]
[ 0 3 0 0 ]]

V. Kolitsas

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Jan 29, 2001, 2:07:21 AM1/29/01
to
Excuse my poor english, and the wrong matrix i gave.
The matrix i mean is the following:
[ 0 1 0 0]
[-1 0 0 0]
[ 0 0 3 1]
[ 0 0 0 3]

for this matrix a error-message occurs, even there are solutions.

Virgil schrieb:

Virgil

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Jan 30, 2001, 12:26:49 AM1/30/01
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In article <3A7516A9...@studserv.Uni-Stuttgart.De>, "V. Kolitsas"
<bil...@studserv.Uni-Stuttgart.De> wrote:

> Excuse my poor english, and the wrong matrix i gave.
> The matrix i mean is the following:
> [ 0 1 0 0]
> [-1 0 0 0]
> [ 0 0 3 1]
> [ 0 0 0 3]
>
> for this matrix a error-message occurs, even there are solutions.

I still get no error messages with the EGV command.

Werner Huysegoms

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Jan 30, 2001, 1:18:07 AM1/30/01
to
In article <Vmhjr-448D37....@news.frii.com>,

But I do...
'Matrix not diagonalizable'
you have to be in exact mode, of course.
and EGVL returns the correct eigenvalues..
definitely a bug here.

--
Best Regards,
Werner Huysegoms


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koud29

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Jan 30, 2001, 3:47:13 AM1/30/01
to

> > > Excuse my poor english, and the wrong matrix i gave.
> > > The matrix i mean is the following:
> > > [ 0 1 0 0]
> > > [-1 0 0 0]
> > > [ 0 0 3 1]
> > > [ 0 0 0 3]

> 'Matrix not diagonalizable'


> you have to be in exact mode, of course.
> and EGVL returns the correct eigenvalues..

confirmed, I get the error too

> definitely a bug here.
I agree

--
This message was written entirely with recycled electrons

Pivo

Christopher P Swider

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Jan 30, 2001, 9:54:49 AM1/30/01
to
3 is a repeated eigenvalue, so unique eigenvectors are not guaranteed.
Thus the matrix has no true diagonal form and the error message is
correct.

JORDAN will give you generalized eigenvectors and a Jordan diagonal
form.

No bug here, as Prof. Parisse will agree.
-Chris

Werner Huysegoms

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Jan 30, 2001, 10:58:43 AM1/30/01
to
In article <3A76D5B9...@nwu.edu>,

Christopher P Swider <csw...@nwu.edu> wrote:
> 3 is a repeated eigenvalue, so unique eigenvectors are not guaranteed.
> Thus the matrix has no true diagonal form and the error message is
> correct.
>
> JORDAN will give you generalized eigenvectors and a Jordan diagonal
> form.
>
> No bug here, as Prof. Parisse will agree.
> -Chris


Mhh it used to be so that the characteristic vectors were returned
in case of repeated eigenvalues, even in symbolic mode ('48 and approx
compatibility). Guess Bernard changed it.
OK, no bug.

--
Best Regards,
Werner Huysegoms

bk

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Jan 30, 2001, 12:11:09 PM1/30/01
to
don't know if bub or not, depends how one look at it.. but a freend of mine
who use version 1,18 finds some eigenvectors, not the right ones... there is
a bug, i am sure. tommorow i will post what eigenvecs he finds out (even we
have the same flags set !).

Werner Huysegoms <werner_h...@my-deja.com> schrieb in im Newsbeitrag:
956obd$750$1...@nnrp1.deja.com...

Parisse Bernard

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Jan 30, 2001, 5:06:09 PM1/30/01
to
Christopher P Swider a écrit :

>
> 3 is a repeated eigenvalue, so unique eigenvectors are not guaranteed.
> Thus the matrix has no true diagonal form and the error message is
> correct.
>
> JORDAN will give you generalized eigenvectors and a Jordan diagonal
> form.
>
> No bug here, as Prof. Parisse will agree.
> -Chris

Yes.
I'm happy to see that there is here someone who has heard of
non diagonalizable matrices and Jordan normal forms!

Werner Huysegoms

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Jan 31, 2001, 1:35:57 AM1/31/01
to
In article <3A773AD1...@fourier.ujf-grenoble.fr>,

Parisse Bernard <par...@fourier.ujf-grenoble.fr> wrote:
> Yes.
> I'm happy to see that there is here someone who has heard of
> non diagonalizable matrices and Jordan normal forms!
>

Here are two post by you, stating that EGV returns characteristic
vectors for multiple eigenvalues (in exact mode):

http://x55.deja.com/[ST_rn=ps]/getdoc.xp?
AN=554331423&CONTEXT=980921296.1047855147&hitnum=1
http://x55.deja.com/[ST_rn=ps]/getdoc.xp?
AN=589820211&CONTEXT=980921296.1047855147&hitnum=0

Granted, the latest applied to ROM 1.17-7 or so. But you did
change 'the rules' somewhere, and I can't seem to find a reference
to it. (probably from 1.18->1.19-1, with the 'new CAS')

--
Best Regards,
Werner Huysegoms

Parisse Bernard

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Jan 31, 2001, 2:26:57 AM1/31/01
to
> Granted, the latest applied to ROM 1.17-7 or so. But you did
> change 'the rules' somewhere, and I can't seem to find a reference
> to it. (probably from 1.18->1.19-1, with the 'new CAS')
>

Yes, the reason was that people repeatedly reported "bugs" because
EGV returned vectors that were not eigenvectors.

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