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Frontiers of Mathematics in China

, Volume 6, Issue 2, pp 363–378 | Cite as

Singular values of nonnegative rectangular tensors

  • Yuning YangEmail author
  • Qingzhi Yang
Research Article

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 

MSC

74B99 15A18 15A69 

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Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Mathematical Sciences and LPMCNankai UniversityTianjinChina

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