The dominant eigenvalue of an essentially nonnegative tensor

L. P. Zhang, Liqun Qi, Z. Y. Luo, Y. Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)


It is well known that the dominant eigenvalue of a real essentially nonnegative matrix is a convex function of its diagonal entries. This convexity is of practical importance in population biology, graph theory, demography, analytic hierarchy process, and so on. In this paper, the concept of essentially nonnegativity is extended from matrices to higher-order tensors, and the convexity and log convexity of dominant eigenvalues for such a class of tensors are established. Particularly, for any nonnegative tensor, the spectral radius turns out to be the dominant eigenvalue and hence possesses these convexities. Finally, an algorithm is given to calculate the dominant eigenvalue, and numerical results are reported to show the effectiveness of the proposed algorithm.
Original languageEnglish
Pages (from-to)929-941
Number of pages13
JournalNumerical Linear Algebra with Applications
Issue number6
Publication statusPublished - 1 Dec 2013


  • Algorithm
  • Convex function
  • Dominant eigenvalue
  • Essentially nonnegative tensor
  • Spectral radius

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics


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