Finding eigenvectors of a matrix when all eigenvalues are known

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.

[Wayne King]

"More specifically I want to keep only eigenvectors with eigenvalue zero"

"all eigenvalues are positive integers"

which statement is true?

[David Holdaway]

The former, I've corrected it

Answer 1

[James Tursa]

Sounds like you are simply looking for the null space of M:

Vset = null(M);

[David Holdaway]

That would be exactly what I am trying to do! Thank you