On copositive matrices with -1, 0, 1 entries

Abstract

Let E be the set of symmetric matrices in which every entry is 0 or ±1 and each diagonal entry is 1. We characterize those matrices in E which are, respectively, (a) copositive, (b) copositive-plus, (c) positive semidefinite. We characterize those copositive matrices in E which are on extreme rays of the cone of copositive matrices. We give a counterexample to a conjecture of L. D. Baumert about zeros of copositive matrices. © 1973.