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arXiv · 1302.6084

The necessary and sufficient conditions of copositive tensors

Yisheng Song·Liqun Qi
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Abstract

In this paper, it is proved that (strict) copositivity of a symmetric tensor $\mathcal{A}$ is equivalent to the fact that every principal sub-tensor of $\mathcal{A}$ has no a (non-positive) negative $H^{++}$-eigenvalue. The necessary and sufficient conditions are also given in terms of the $Z^{++}$-eigenvalue of the principal sub-tensor of the given tensor. This presents a method of testing (strict) copositivity of a symmetric tensor by means of the lower dimensional tensors. Also the equivalent definition of strictly copositive tensors is given on entire space $\mathbb{R}^n$.

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Yisheng Song, Liqun Qi. 2013-02-25. The necessary and sufficient conditions of copositive tensors. https://doi.org/10.1080/03081087.2013.851198

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