Re: eignenvalue for nonsymmetric matrix

[Mike Miller]

On Thu, 7 Apr 2005, 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.

If it's not of full rank, it has some zero eigenvalues.  eig still works 
for matrices of less than full rank.  On my system, using old Octave, eig 
returns this:

   -2.2094e+00
    3.6209e+01
   -1.3449e-16
   -3.1818e-15

Mike



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