Abstract
Let be a normal matrix with spectrum , and let be a perturbed matrix with spectrum . If is still normal, the celebrated Hoffman–Wielandt theorem states that there exists a permutation π of such that , where denotes the Frobenius norm of a matrix. This theorem reveals the strong stability of the spectrum of a normal matrix. However, if A or is non-normal, the Hoffman–Wielandt theorem does not hold in general. In this paper, we present new upper bounds for , provided that both A and are general matrices. Some of our estimates improve or generalize the existing ones.
Disclosure statement
No potential conflict of interest was reported by the author(s).