Inertia sets of two classes of symmetric sign patterns

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.