Re: eignenvalue for nonsymmetric matrix

[Vic Norton]

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 http://www.cis.rit.edu/~ejipci/Reports/svd.pdf for
> details.



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