Necessary and sufficient conditions

Abstract

Abstract. In this paper, it is proved that a symmetric tensor is (strictly) copositive if and only if each of its principal subtensors has no (non-positive) negative H ++ -eigenvalue. Necessary and sufficient conditions for (strict) copositivity of a symmetric tensor are also given in terms of Z ++ -eigenvalues of the principal sub-tensors of that tensor. This presents a method for testing (strict) copositivity of a symmetric tensor by means of lower dimensional tensors. Also an equivalent definition of strictly copositive tensors is given on the entire space R n .