Hypergraph characterizations of copositive tensors

A real symmetric tensor A=(ai_(1…im))∈R^([m,n]) is copositive(resp.,strictly copositive)if Ax^(m)≥0(resp.,Ax^(m)>0)for any nonzero nonnegative vector x∈ℝ^(n).By using the associated hypergraph of A,we give necessary and sufficient conditions for the copositivity of A.For a real symmetric tensor A satisfying the associated negative hypergraph H−(A)and associated positive hypergraph H+(A)are edge disjoint subhypergraphs of a supertree or cored hypergraph,we derive criteria for the copositivity of A.We also use copositive tensors to study the positivity of tensor systems.