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
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 ]]
for this matrix a error-message occurs, even there are solutions.
Virgil schrieb:
> 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.
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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> > > 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
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
Werner Huysegoms <werner_h...@my-deja.com> schrieb in im Newsbeitrag:
956obd$750$1...@nnrp1.deja.com...
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
Yes, the reason was that people repeatedly reported "bugs" because
EGV returned vectors that were not eigenvectors.