Criteria for copositive matrices using simplices and barycentric coordinates

Abstract

We present criteria for verifying the copositivity of an n × n matrix, given that all its principal submatrices of order n - 1 are copositive. For n = 4, 5 necessary and sufficient conditions for copositivity are given, based on the sign distribution of the off-diagonal elements of a single row. Here it is only assumed that one principal submatrix is copositive. © 1995 Elsevier Science Inc.