Standard tensor and its applications in problem of singular values of tensors

doi:10.1007/s11464-019-0786-4

Front. Math. China

2019, Vol. 14

Issue (5) : 967-987 https://doi.org/10.1007/s11464-019-0786-4

RESEARCH ARTICLE

Standard tensor and its applications in problem of singular values of tensors

Qingzhi YANG^1,²(

), Yiyong LI²

¹. School of Mathematics and Statistics, Kashi University, Kashi 844006, China
². School of Mathematical Sciences, Nankai University, Tianjin 300071, China

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Abstract

In this paper, first we give the definition of standard tensor. Then we clarify the relationship between weakly irreducible tensors and weakly irreducible polynomial maps by the definition of standard tensor. And we prove that the singular values of rectangular tensors are the special cases of the eigen-values of standard tensors related to rectangular tensors. Based on standard tensor, we present a generalized version of the weak Perron-Frobenius Theorem of nonnegative rectangular tensors under weaker conditions. Furthermore, by studying standard tensors, we get some new results of rectangular tensors. Besides, by using the special structure of standard tensors corresponding to nonnegative rectangular tensors, we show that the largest singular value is really geometrically simple under some weaker conditions.

Keywords Standard tensor nonnegative rectangular tensor singular value geometrically simple

Corresponding Author(s): Qingzhi YANG

Issue Date: 22 November 2019

Cite this article:

Qingzhi YANG,Yiyong LI. Standard tensor and its applications in problem of singular values of tensors[J]. Front. Math. China, 2019, 14(5): 967-987.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0786-4
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I5/967

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