Singular values of nonnegative rectangular tensors

doi:10.1007/s11464-011-0108-y

Front Math Chin

2011, Vol. 6

Issue (2) : 363-378 https://doi.org/10.1007/s11464-011-0108-y

RESEARCH ARTICLE

Singular values of nonnegative rectangular tensors

Yuning YANG, Qingzhi YANG(

)

School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, 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. Some properties concerning the singular values of a real rectangular tensor were discussed by K. C. Chang et al. [J. Math. Anal. Appl., 2010, 370: 284-294]. In this paper, we give some new results on the Perron-Frobenius Theorem for nonnegative rectangular tensors. We show that the weak Perron-Frobenius keeps valid and the largest singular value is really geometrically simple under some conditions. In addition, we establish the convergence of an algorithm proposed by K. C. Chang et al. for finding the largest singular value of nonnegative primitive rectangular tensors.

Keywords Nonnegative rectangular tensor Perron-Frobenius Theorem singular value algorithm

Corresponding Author(s): YANG Qingzhi,Email:qz-yang@nankai.edu.cn

Issue Date: 01 April 2011

Cite this article:

Yuning YANG,Qingzhi YANG. Singular values of nonnegative rectangular tensors[J]. Front Math Chin, 2011, 6(2): 363-378.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-011-0108-y
https://academic.hep.com.cn/fmc/EN/Y2011/V6/I2/363

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