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Re: eignenvalue for nonsymmetric matrix

From: Vic Norton
Subject: Re: eignenvalue for nonsymmetric matrix
Date: Thu, 7 Apr 2005 16:05:02 -0400

svd gives you singular values, not eigen values. Generally you cannot get an eigenvalue decomposition from a singular value decomposition. The singular value decomposition is an orthogonal decomposition and very robust. Distinct eigenvectors, on the other hand, may be almost colinear. Orthogonality plays no roll here. The eigenvalue problem can be very tricky, very sensitive to small perturbations.

At 12:27 PM -0400 4/7/05, Przemek Klosowski wrote:
   a non-symmetric full matrix. Octave gives me the following error:
   error: dgeev failed to converge. The sample problem is below.

   octave:1> stiff = [1,2,3,4;5,6,7,8;9,10,11,12;13,14,15,16]
   octave:2> eig(stiff)
   error: dgeev failed to converge

that is because the matrix you have picked up is degenerate, i.e.
its rows are linearly dependent. In fact, it has only two independent
rows, as you can see by executing rank(stiff). The eig() function only
works for non-degenerate matrices; for degenerate ones you should
use svd(). See for

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