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arXiv · 1706.00944

Exclusion sets in eigenvalue inclusion sets for tensors

Chaoqian Li·Suhua Li·Qingbing Liu·Yaotang Li
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Abstract

By excluding some sets, which don't include any eigenvalue of a tensor, from some existing eigenvalue inclusion sets, two new sets are given to locate all eigenvalues of a tensor. And it is shown that these two sets are contained in the Geršgorin eigenvalue inclusion set of tensors provide by Qi (Journal of Symbolic Computation 2005; 40:1302-1324) and the Brauer-type eigenvalue inclusion set provide by Li et al. (Numer. Linear Algebra Appl. 2014; 21:39-50) respectively. Two sufficient conditions such that the determinant of a tensor is not zero are also provided.

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Chaoqian Li, Suhua Li, Qingbing Liu, Yaotang Li. 2017-06-03. Exclusion sets in eigenvalue inclusion sets for tensors. https://arxiv.org/abs/1706.00944

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