Sign patterns of nonnegative normal matrices

Abstract

By a nonnegative sign pattern we mean a matrix whose entries are from the set {+, 0}. A nonnegative sign pattern A is said to allow normality if there is a normal matrix B whose entries have signs indicated by A. In this paper the combinatorial structure of nonnegative normal matrices, in particular, (0, 1) normal matrices, is investigated. Among other results, up to order 5, (0, 1) normal matrices are classified up to permutation similarity. A number of general conditions for sign patterns to allow normality are obtained. Some interesting constructions of nonnegative normal matrices are provided. In particular, a number of bordering results are obtained. Some open problems are also indicated. © Elsevier Science Inc., 1997.