From: Axel Etzold <AEtzold@...>
Date: 2007-11-23T03:19:05+09:00
Subject: Re: eigenvector discrepency was (Re: [Matrix] eigenvalues, eigenvectors in Ruby ???)


-------- Original-Nachricht --------
> Datum: Fri, 23 Nov 2007 02:35:01 +0900
> Von: unbewusst.sein@weltanschauung.com.invalid
> An: ruby-talk@ruby-lang.org
> Betreff: Re: eigenvector discrepency was (Re: [Matrix] eigenvalues, eigenvectors in Ruby ???)

> Axel Etzold <AEtzold@gmx.de> wrote:
> 
> > 
> > Yes, but that's not what I meant, as you can have different vectors
> > mapped to the same vector under a matrix mapping.
> > You'd have to check, whether, for a matrix m, the following holds:
> > 
> > for each v that is an eigenvector to m, and each corresponding
> eigenvalue
> > c (vectors and numbers as delivered by the software),
> > 
> > m*v=c*v .
> 
> 
> i did verify that, that' OK for two different matrices (a and b).
> however those two matrices are different within a permutation which
> normally (OK with GSL) i could find the permutation matrix p such that :
> 
> p * a * p^(-1) = b
> 
> this permutation matrix being computed by comparing an eigenvector of a
> with the corresponding of b (same values different order) which i kind
> find in case of ExtendMatrix...
> 
> -- 
> Une B�vue

What is the problem that you are actually trying to solve ?
Why do you compute eigenvectors to permutation matrices ? A permutation
matrix will always be unitary and thus won't change the eigenvectors
(up to ordering, of course). For the construction of eigenvectors, you
can look up the Gram-Schmidt orthogonalization ( or orthonormalization)
method, but I think you're now doing something that requires a lot of
computation (finding eigenvectors requires solving a linear equation system), which you could probably do without ...

Best regards,

Axel 

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