Nonnegative tensors revisited: plane stochastic tensors

Maolin Che, Changjiang Bu, Liqun Qi, Yimin Wei

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)


In this paper, we develop and enrich the theory of nonnegative tensors. We define the sign nonsingular tensors and establish the relationship between the combinatorial determinant and the permanent of nonnegative tensors. We generalize the results from doubly stochastic matrices to totally plane stochastic tensors and obtain a probabilistic algorithm for locating a positive diagonal in a nonnegative tensor under certain conditions. We form a normalization algorithm to convert some nonnegative tensors to plane stochastic tensors. We obtain a lower bound for the minimum of the axial N-index assignment problem by means of the set of plane stochastic tensors.

Original languageEnglish
Pages (from-to)1364-1391
Number of pages28
JournalLinear and Multilinear Algebra
Issue number7
Publication statusPublished - 3 Jul 2019


  • combinatorial determinant
  • diagonal product
  • Nonnegative tensor
  • normalization algorithm
  • plane stochastic tensors
  • positive diagonal
  • sign nonsingular tensor
  • tensor permanent

ASJC Scopus subject areas

  • Algebra and Number Theory


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