Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/77527
Title: Column sufficient tensors and tensor complementarity problems
Authors: Chen, H
Qi, L 
Song, Y
Keywords: Column sufficient tensor
H-eigenvalue
Handicap
Tensor complementarity problems
Issue Date: 2018
Publisher: Higher Education Press
Source: Frontiers of mathematics in China, 2018, v. 13, no. 2, p. 255-276 How to cite?
Journal: Frontiers of mathematics in China 
Abstract: Stimulated by the study of sufficient matrices in linear complementarity problems, we study column sufficient tensors and tensor complementarity problems. Column sufficient tensors constitute a wide range of tensors that include positive semi-definite tensors as special cases. The inheritance property and invariant property of column sufficient tensors are presented. Then, various spectral properties of symmetric column sufficient tensors are given. It is proved that all H-eigenvalues of an even-order symmetric column sufficient tensor are nonnegative, and all its Z-eigenvalues are nonnegative even in the odd order case. After that, a new subclass of column sufficient tensors and the handicap of tensors are defined. We prove that a tensor belongs to the subclass if and only if its handicap is a finite number. Moreover, several optimization models that are equivalent with the handicap of tensors are presented. Finally, as an application of column sufficient tensors, several results on tensor complementarity problems are established.
URI: http://hdl.handle.net/10397/77527
ISSN: 1673-3452
EISSN: 1673-3576
DOI: 10.1007/s11464-018-0681-4
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