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Journal Article
Hypergraph characterizations of copositive tensors
2021
Overview
A real symmetric tensor A=(ai1…im)∈ℝ[m,n] is copositive (resp., strictly copositive) if Axm⩾0 (resp., Axm>0 ) for any nonzero nonnegative vector x ∈ ℝn. 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.
Publisher
Springer Nature B.V
Subject
