eigenvector on singlar matrix

[Takuya Sekikawa]

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
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