From: Axel Etzold Date: 2007-11-24T06:13:20+09:00 Subject: Re: eigenvector discrepency was (Re: [Matrix] eigenvalues, eigenvectors in Ruby ???) -------- Original-Nachricht -------- > Datum: Fri, 23 Nov 2007 19:30:02 +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 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 ! Glad to help :) My numerics textbook gives some references for the amount of calculations needed for both QR and Jacobi. The convergence of QR is quadratic (Henrici, SIAM J Applied Mathematics 6 (1958) 144-162), Sch�nhage A., Numer. Math. 3 (1961) 374-380, The convergence of the QR method is actually cubic for bigger sized n, (Gourlay, Watson, Computational methods for matrix eigenproblems, John Wiley, London, 1973; Wilkinson, Lin. Alg. and Its Appl., 1(1968), 409-20. These considerations are actually for really big matrices, not for 4x4 ones - maybe if you had to calculate symmetries of the DNA or something ? Best regards, Axel > > -- > Une B�vue -- Ist Ihr Browser Vista-kompatibel? Jetzt die neuesten Browser-Versionen downloaden: http://www.gmx.net/de/go/browser