Necessary and Sufficient Conditions for Copositive Tensors
نویسندگان
چکیده
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 Rn.
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Article history: Received 6 December 2012 Accepted 11 March 2013 Available online 8 April 2013 Submitted by R.A. Brualdi AMS classification: 15A18 15A69
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