Necessary and sufficient conditions for copositive tensors

Yisheng Song, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

37 Citations (Scopus)

Abstract

In this paper, it is proved that a symmetric tensor is (strictly) copositive if and only if each of its principal sub-tensors has no (non-positive) negative (Formula presented.) -eigenvalue. Necessary and sufficient conditions for (strict) copositivity of a symmetric tensor are also given in terms of (Formula presented.) -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 (Formula presented.).
Original languageEnglish
Pages (from-to)120-131
Number of pages12
JournalLinear and Multilinear Algebra
Volume63
Issue number1
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • copositive tensors
  • H -eigenvalue ++
  • principal sub-tensor
  • Z -eigenvalue ++

ASJC Scopus subject areas

  • Algebra and Number Theory

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