Title

Preservers of eigenvalue inclusion sets

Document Type

Article

Department/Program

Mathematics

Journal Title

Linear Algebra and Its Applications

Pub Date

2010

Volume

433

Issue

5

First Page

1038

Abstract

For a square matrix A, let S(A) be an eigenvalue inclusion set such as the Gershgorin region, the Brauer region in terms of Cassini ovals, and the Ostrowski region. Characterization is obtained for maps ch on n x n matrices satisfying S(phi(A) - phi(B)) = S(A - B) for all matrices A and B. From these results, one can deduce the structure of additive or (real) linear maps satisfying S(A) = S(phi(A)) for every matrix A. (C) 2010 Elsevier Inc. All rights reserved.

DOI

10.1016/j.laa.2010.04.028

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