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RE: different eigenvectors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg83921] RE: [mg83883] different eigenvectors
  • From: "Jaccard Florian" <Florian.Jaccard at he-arc.ch>
  • Date: Tue, 4 Dec 2007 04:30:43 -0500 (EST)
  • References: <200712031208.HAA26078@smc.vnet.net>

Sure!

Eigenvectors just give the directions!
As you know, if v is an eigenvector of the matrix A, you have : 
A*v=lambda*v, where lambda is the eigenvalue associated to v.

If you take another vector with the same direction, for example -3*v, it 
is also an eigenvector associated to lambda, because 
A*(-3v)=-3*(A*v)=-3*lambda*v=lambda*(-3v).

So, if you take another system, you surely can obtain another vector!

If two vectors are associated to the same eigenvalue, let us say v and 
w, then all the combinaisons (like a*v+b*w) are eigenvectors. So it can 
become quite difficult to see that results are equivalent.

You have to see the eigenvectors as directions, and not vectors.
The important thing is to see what eigenvalue are associated to what 
collection of eigendirections.

The best thing is to use :

Eigensystem[A]//MatrixForm

The first line are the eigenvalues, the second, in the same order, the 
eigendirections.

Regards

F.Jaccard






-----Message d'origine-----
De=A0: vicky Al Aisa [mailto:vickyisai at gmail.com]
Envoy=E9=A0: lundi, 3. d=E9cembre 2007 13:09
=C0=A0: mathgroup at smc.vnet.net
Objet=A0: [mg83883] different eigenvectors

hello

I am using Eigenvectors function to calculate eigenvectors in
mathematica 5.2.
while comparing the results with the eigenvectors (of same matrix)
computed in another system, i found that both the results are bit =
different
with some values having opposite sign and coloumns rearranged.

thank you
viky al aisa



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