Inertia sets of two classes of symmetric sign patterns*1

Abstract

A sign pattern is a matrix whose entries are from the set {+,−,0}. For a symmetric sign pattern A of order n , the inertia set of A is the set of inertias of all real symmetric matrices with the same sign pattern as A . The purpose of this paper is to characterize the inertia sets of symmetric star and nonnegative symmetric tridiagonal sign patterns.