Ah, sorry, I should have clarified. This is the Hamilotnian of a quantum system. You compute the time evolution using the eigenvectors, I would like to plot a 3d graph of z vs t to find out how sensitive the system is to perturbations (eigenvector perturbation theory for these matrices is a bit difficult with a pen and paper.....).

Having used your suggestion of using the characteristic polynomial to get the eigenvalues, I think I've worked out what the problem is, I get a lambda = RootOf equation where coefficients of z have 21 digits. My suspicion is that somewhere in the Eigenvector calculation the numbers become too large to be stored on the computer- returning NaN which would be why somehwere along the way something doesn't evaluate to float. Does this sound like a sensible explanation? I hope I'm wrong because I really would like to calculate this!!!!!

Ah, sorry, I should have clarified. This is the Hamilotnian of a quantum system. You compute the time evolution using the eigenvectors, I would like to plot a 3d graph of z vs t to find out how sensitive the system is to perturbations (eigenvector perturbation theory for these matrices is a bit difficult with a pen and paper.....).

Having used your suggestion of using the characteristic polynomial to get the eigenvalues, I think I've worked out what the problem is, I get a lambda = RootOf equation where coefficients of z have 21 digits. My suspicion is that somewhere in the Eigenvector calculation the numbers become too large to be stored on the computer- returning NaN which would be why somehwere along the way something doesn't evaluate to float. Does this sound like a sensible explanation? I hope I'm wrong because I really would like to calculate this!!!!!