Inertia sets of symmetric 2-generalized star sign patterns

Abstract

A sign pattern is a matrix whose entries are from the set {+−0}. Associated with each sign pattern A is a qualitative class of matrices Q(A). For a symmetric sign pattern A of order n, the inertia set of A is the set , and the symmetric inertia set , where i(B) is the inertia of B. In this article we characterize the symmetric 2-generalized star sign patterns that require unique (symmetric) inertia, and also give the (symmetric) inertia set of a symmetric 2-generalized star sign pattern.