Frontiers of Mathematics in China

, Volume 8, Issue 1, pp 63–83 | Cite as

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

Research Article
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Accepted:

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 study the singular values/vectors problem of real nonnegative partially symmetric rectangular tensors. We first introduce the concepts of l k,s -singular values/vectors of real partially symmetric rectangular tensors. Then, based upon the presented properties of l k,s -singular values /vectors, some properties of the related l k,s -spectral radius are discussed. Furthermore, we prove two analogs of Perron-Frobenius theorem and weak Perron-Frobenius theorem for real nonnegative partially symmetric rectangular tensors.

Keywords

Nonnegative rectangular tensor lk,s-singular value lk,s-spectral radius irreducibility weak irreducibility 

MSC

15A18 15A69 90C30 
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Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of ScienceHangzhou Dianzi UniversityHangzhouChina
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHong KongChina

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