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Finding eigenvectors of a matrix when all eigenvalues are known

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I am currently running a code that has to diagonalise a large number of matrices every run. From other considerations I know what all the eigenvalues of these matrices will be before this calculation start (up to some eps level round off introduced by the code), this there any way I can use this to speed up the diagonalisation?
More specifically I want to keep only eigenvectors with eigenvalue zero, of which there are, say, "n" and denote the set off all such vectors as "Vset". Let us call the matrix 'M' then I wish to solve the problem:
M*Vset = zeros(size(Vset))
(Linsolve doesn't seem to work for this problem!)
Edit: Also all my matrix elements are double precision and real, all eigenvalues are non-negative integers and all eigenvectors will be real, also the matrix is not sparse.
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Accepted Answer

James Tursa
James Tursa on 8 May 2012
Sounds like you are simply looking for the null space of M:
Vset = null(M);

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