Having the eigenvalue of my matrix (Hamiltonian), how can I get the eigenvector associated with it?

Hello, I have a given eigenvalue (energy) of my matrix (Hamiltonian), which is known. Now I want to obtain the eigenvector associated with it? Is there any function similar to eig to do so? Thanks in advance.

Answer 1

[Matt J]

V=null(A-eigenvalue*eye(size(A))

[John D'Errico]

A virtue of this solution is that if the eigenvalue has multiplicity greater than 1, then V will contain all the eigenvectors associated with that eigenvalue.

A = ones(3);

A has one eigenvalue of 3, but 0 is an eigenvalue, with multiplicity 2.

null(A-3*eye(size(A)))
ans =
     -0.57735
     -0.57735
     -0.57735

null(A-0*eye(size(A)))
ans =
            0       0.8165
     -0.70711     -0.40825
      0.70711     -0.40825

[Auryn_]

Thanks!