The numerical range of a nonnegative matrix

Abstract

We offers an almost self-contained development of Perron-Frobenius type results for the numerical range of an (irreducible) nonnegative matrix, rederiving and completing the previous work of Issos, Nylen and Tam, and Tam. and Yang on this topic. We solve the open problem of characterizing nonnegative matrices whose numerical ranges are re gular convex polygons with center at the origin. Some related results are obtained and some open problems are also posed. (C) 2002 Elsevier Science Inc. All rights reserved.