Preservers of eigenvalue inclusion sets of matrix products

Nung-Sing Sze
Virginia Forstall, William & Mary
Aaron Herman, William & Mary
Chi-Kwong Li, William & Mary
Vincent Yannello, William & Mary

Abstract

For a square matrix A, let S(A) be an eigenvalue inclusion set such as the Gershgorin region, the union of Cassini ovals, and the Ostrowski's set. Characterization is obtained for maps Phi on n x n matrices satisfying S(Phi(A)Phi(B)) = S(AB) for all matrices A and B. (C) 2010 Elsevier Inc. All rights reserved.