Inertia sets of symmetric 2-generalized star sign patterns

摘要

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 i(A) = {i(B) vertical bar B is an element of Q(A)}, and the symmetric inertia set si(A) = {i(B) vertical bar B = B-T is an element of Q(A)}, 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.