Bounds for the spectrum of normal matrices

Abstract

Let A be a normal matrix with eigenvalues λ1, λ2,..., λn, and let G{cyrillic} denote the smallest disc containing these eigenvalues. We give some inequalities relating the center and radius of G{cyrillic} to the entries in A. When applied to Hermitian matrices our results give lower bounds on the spread maxij(λi - λj) of A. When applied to positive definite Hermitian matrices they give lower bounds on the Kantorovich ratio maxij(λi - λj)/(λi + λj). © 1994.