An algorithm for the inertia sets of tree sign patterns

Abstract

A matrix whose entries are +, ¡ or 0 is said a sign pattern. The inertia set of an n-by-n symmetric sign pattern A is the set of inertias of all real symmetric matrices with the same sign pattern as A. We present an algorithm to compute the inertia set of any symmetric tree (or acyclic) sign pattern. The procedure generalizes some recent results. Some examples are provided.