Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/30330
Title: Necessary and sufficient conditions for copositive tensors
Authors: Song, Y
Qi, L 
Keywords: Copositive tensors
H++-eigenvalue
Principal sub-tensor
Z++-eigenvalue
Issue Date: 2013
Publisher: Taylor & Francis
Source: Linear and multilinear algebra, 2013, v. 63, no. 1, p. 120-131 How to cite?
Journal: Linear and multilinear algebra 
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.).
URI: http://hdl.handle.net/10397/30330
ISSN: 0308-1087
EISSN: 1563-5139
DOI: 10.1080/03081087.2013.851198
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