different eigenvalues from np.eig and np.svd

Question

I'm comparing the eigenvalues computed by np.eig(np.dot(A.T, A))**2 and np.eig(A). I found some values are the same but some are not. Can anybody tell me why would this happen?

Answer 1

There is no mathematical reason to expect that the eigenvalues of A should be equal to the squares of the eigenvalues of (A.T * A). For example, the eigenvalues of A might be complex, whereas the eigenvalues of A.T * A are guaranteed to be real because A.T * A is a symmetric matrix.