Question: are eigenvalues of a and a−1 are related?
Answer: A matrix A has an inverse matrix A - 1 if and only if it does not have zero as an eigenvalue. If 1 , ..., n 0 are the eigenvalues of A, then the eigenvalues of A - 1 are 1 / 1 , ..., 1 / n . Proof. ... => 1 / is an eigenvalue of A-1 (with as a corresponding eigenvalue).