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
instead of SLEPc.
For large matrices, if the dimension of the nullspace is small then
you should have no problems when computing the eigenvectors of zero
eigenvalues with SLEPc. But if you have a large nullspace then things
may get problematic - I have not tried this case. Please report any
problems to the SLEPc maintainance email.
Jose
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