lk,s-Singular values and spectral radius of partially symmetric rectangular tensors

doi:10.1007/s11464-015-0494-7

Front. Math. China

2016, Vol. 11

Issue (3) : 605-622 https://doi.org/10.1007/s11464-015-0494-7

RESEARCH ARTICLE

l^k,s-Singular values and spectral radius of partially symmetric rectangular tensors

Hongmei YAO(

),Bingsong LONG,Changjiang BU,Jiang ZHOU

College of Science, Harbin Engineering University, Harbin 150001, China

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Abstract

The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we first study properties of lk,s-singular values of real rectangular tensors. Then, a necessary and sufficient condition for the positive definiteness of partially symmetric rectangular tensors is given. Furthermore, we show that the weak Perron-Frobenius theorem for nonnegative partially symmetric rectangular tensor keeps valid under some new conditions and we prove a maximum property for the largest lk,s-singular values of nonnegative partially symmetric rectangular tensor. Finally, we prove that the largest lk,ssingular value of nonnegative weakly irreducible partially symmetric rectangular tensor is still geometrically simple.

Keywords l^k,s-Singular values spectral radius positive definiteness partially symmetric rectangular tensor weakly irreducible

Corresponding Author(s): Hongmei YAO

Issue Date: 17 May 2016

Cite this article:

Hongmei YAO,Bingsong LONG,Changjiang BU, et al. l^k,s-Singular values and spectral radius of partially symmetric rectangular tensors[J]. Front. Math. China, 2016, 11(3): 605-622.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0494-7
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I3/605

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