Spectral properties of positively homogeneous operators induced by higher order tensors.

Yisheng Song, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

57 Citations (Scopus)


The Fredholm alternative type results are proved for eigenvalues (E-eigenvalues, H-eigenvalues, Z-eigenvalues) of a higher order tensor A. For the positively homogeneous operators FA and TA induced by a higher order tensor A, we show some relationship between the Gelfand formula and the spectral radius, and present the upper bound of their spectral radii. Furthermore, for a nonnegative tensor A, we obtain the practical relevance for the spectral radius of the operators FA and TA as well as the operator norms of FA and TA.
Original languageEnglish
Pages (from-to)1581-1595
Number of pages15
JournalSIAM Journal on Matrix Analysis and Applications
Issue number4
Publication statusPublished - 1 Dec 2013


  • Eigenvalue-eigenvector
  • Fredholm alternative
  • Gelfand formula
  • Higher order tensor
  • Positively homogeneous

ASJC Scopus subject areas

  • Analysis

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