# eigenvector on singlar matrix

Jose E. Roman jroman at dsic.upv.es
Tue Jul 28 02:57:58 CDT 2009

```On 28/07/2009, Takuya Sekikawa wrote:

> Hi
>
> I have a question about SLEPc.
>
> What are EigenVectors calculated when given matrix is singular?
>
> (ex1)
> for example, matrix like this:
>
>    (1 1 1)
> A = (1 1 1)
>    (1 1 1)
>
> matrix A have 2 eigenvalues, one is 0 (double multiple root),
> and other is 3.
>
> in this case eigenvector related to eigenvalue 0, is
> (z1, z2, -(z1+z2))t (z1, z2 can be any value. i.e. freedom degree is
> 2)
>
>
> (ex2)
>
> B = (0 1)
>    (0 0)
>
> in this case B's eigenvalue is only 0. (double multiple root)
> but eigenvector has only 1 freedom degree.
> (z1, 0)t
>
> My question is, what will be solution by SLEPc in these case?
>
> Thanks,
> Takuya
> ---------------------------------------------------------------
>  Takuya Sekikawa
>         Mathematical Systems, Inc
>                    sekikawa at msi.co.jp
> ---------------------------------------------------------------

For such small matrices, the computed solution will be the same as the
one provided by Lapack. If your problem matrices are small, use Lapack