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

Chen Ling, Liqun Qi

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5 Citations (Scopus)


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 lk,s-singular values/vectors of real partially symmetric rectangular tensors. Then, based upon the presented properties of lk,s-singular values /vectors, some properties of the related lk,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.
Original languageEnglish
Pages (from-to)63-83
Number of pages21
JournalFrontiers of Mathematics in China
Issue number1
Publication statusPublished - 14 Jan 2013


  • irreducibility
  • l -singular value k,s
  • l -spectral radius k,s
  • Nonnegative rectangular tensor
  • weak irreducibility

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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