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).