On the generalized inverse of a copositive matrix

Abstract

ABSTRACT We show that a real symmetric matrix A with spectral radius ρ and all negative eigenvalues equal to is copositive if and only if the eigenspaces of and ρ have some special properties, and and that such matrices are exactly the indefinite copositive matrices satisfying a known sufficient condition for the copositivity of the (Moore-Penrose generalized) inverse of A. It is also shown that for every and there exist such copositive matrices where the multiplicity of is k.