RE: [Help-gsl] eigenvectors of non symmetric matrix?

[Warren Weckesser]

Don't use a gsl_eigen_* function to find the eigenvalues and eigenvectors.

The matrix a*b^T has rank 1.  The only nonzero eigenvalue is b^T*a (i.e. the 
dot product of b and a), and the corresponding eigenvector is a.

The eigenspace of the zero eigenvalue is the set of all vectors normal to b, 
i.e. x such that b^T*x = 0, so just find a basis for this space to get the 
eigenvectors of the zero eigenvalue.

--Warren

________________________________________
From: address@hidden address@hidden On Behalf Of David Doria address@hidden
Sent: Thursday, March 06, 2008 5:08 PM
To: address@hidden
Subject: [Help-gsl] eigenvectors of non symmetric matrix?

I am taking an outer product:

a b^T
where a and b are column vectors.  Then I want the eigen values and vectors
of the resulting matrix (called mat3).

I tried to use:
    gsl_eigen_symmv_workspace * EigenWorkspace = gsl_eigen_symmv_alloc (2);
    gsl_eigen_symmv (mat3, EigenValues, EigenVectors, EigenWorkspace);

but it gave the wrong results.  I guess this is because it was expecting a
symmetric matrix? Is the only other choice to use:
    gsl_eigen_hermv_workspace * EigenWorkspace = gsl_eigen_hermv_alloc (2);
    gsl_eigen_hermv (mat3, EigenValues, EigenVectors, EigenWorkspace);

but for that, I'd have to first make mat3 a complex matrix (or so says the
error haha)?

Please let me know.

--
Thanks,

David
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