From: "M. Edward (Ed) Borasky" <znmeb@...>
Date: 2007-11-24T03:14:04+09:00
Subject: Re: eigenvector discrepency was (Re: [Matrix] eigenvalues, eigenvectors in Ruby ???)

Une B�vue wrote:
> Axel Etzold <AEtzold@gmx.de> wrote:
> 
>> The permutation matrices are rotation matrices 
>> (http://en.wikipedia.org/wiki/Rotation_matrix), 
>> if and only if the permutation is even (the number 
>> of elements exchanged is even). Then, they can be 
>> decomposed into rotations of 45 degrees 
>> (i.e. exchanges of coordinates x,y different planes).
>> See also the article about orthogonal matrices :
>> http://en.wikipedia.org/wiki/Orthogonal_matrix
>>
> 
> [...]
> 
>> The original is in German: Kombinatorische Anzahlbestimmungen f�r Gruppen,
>> Graphen und chemische Verbindungen, Acta Mathematica, 68 (1937), 145-254,
>> whichever you prefer :)
> 
> fine thanks a lot for all your references, i think as the name implies
> for eigenvalues (@eigval = @extendmatrix.eigenvaluesJacobi) that's a
> Jacobi method which i don't know for GSL.
> 
> Vielen dank !

Interesting ... the Jacobi method was for many years the most commonly 
used method for diagonalizing a real symmetric matrix (another term for 
finding its eigenvalues and eigenvectors). The modern methods based on 
QR operations are more efficient, so they are now the methods of choice.