Re: Eigenvalues computation

[Daniel Heiserer]

Daniel Tourde wrote:
> 
> Hi !
> 
> I would like to trace the variation of the eigenvalues of a matrix D(k)
> in function of k. Until now I have considered that Octave kept the same
> order for my eigenvalues but in view of some strange results I have I'm
> wondering if at a certain step of my computation the order does not
> change (lambda8 <-> lambda9 for instance).
> 
> So, here is my question :
> Does octave classify the eigenvalues of a matrix ?
> If yes, how ?
> If yes, how can I force Octave to keep this classification all along my
> computation of lambda(k) x = D(k) x ?
> If no, what can I do ? ....
> 
> Thanks for any answer. Best regards

Hi. What is an eigenvalue (in a physical sense)? It's not only a
mathematical solution of solving the saekular-equation det(A-L1)=0!. In
fact an eigenvalue describes some geometry ==> eigenvector. If you are
looking on eigenvalues only you probably assume that the eigenvectors
don't change or change only a little so you could map the old values to
the new values. But anyway they are not equivalent, because their
"shapes" change also (even slightly). So if you want to trace
eigenvalues don't look at the values first, look at their shapes
(eigenvectors).

[value_1,shape_1=eig(mymatrix(x1));
[value_2,shape_2=eig(mymatrix(x2));

just make the scalar product of the new shapes with the old shapes:

mac=shape_1*shape_2';

the mac (modal assurance criterion) then tells you if (if their index is
close to 1) and how (look at the indices) you can correlate the old and
the new shapes. Bye correlating the shapes you can look at their
eigenvalues and you are done.

Have a nice day.

Bye                        Daniel
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Daniel Heiserer, BMW AG, Knorrstrasse 147, 80788 Muenchen
Abteilung EK-20
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