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


From: David Doria
Subject: Re: [Help-gsl] eigenvectors of non symmetric matrix?
Date: Thu, 6 Mar 2008 19:24:08 -0500

I actually am going to sum a bunch of rank 1 matrices before I find the
eigen vectors, so there will be a full rank matrix before the
eigenvecs/values are found.

Thanks for the suggestions though!

Dave

On Thu, Mar 6, 2008 at 7:00 PM, Warren Weckesser <
address@hidden> wrote:

> 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
> _______________________________________________
> Help-gsl mailing list
> address@hidden
> http://lists.gnu.org/mailman/listinfo/help-gsl
>



-- 
Thanks,

David


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