Column sufficient tensors and tensor complementarity problems

Haibin Chen, Liqun Qi, Yisheng Song

Research output: Journal article publicationJournal articleAcademic researchpeer-review

57 Citations (Scopus)


Stimulated by the study of sufficient matrices in linear complementarity problems, we study column sufficient tensors and tensor complementarity problems. Column sufficient tensors constitute a wide range of tensors that include positive semi-definite tensors as special cases. The inheritance property and invariant property of column sufficient tensors are presented. Then, various spectral properties of symmetric column sufficient tensors are given. It is proved that all H-eigenvalues of an even-order symmetric column sufficient tensor are nonnegative, and all its Z-eigenvalues are nonnegative even in the odd order case. After that, a new subclass of column sufficient tensors and the handicap of tensors are defined. We prove that a tensor belongs to the subclass if and only if its handicap is a finite number. Moreover, several optimization models that are equivalent with the handicap of tensors are presented. Finally, as an application of column sufficient tensors, several results on tensor complementarity problems are established.
Original languageEnglish
Pages (from-to)255-276
Number of pages22
JournalFrontiers of Mathematics in China
Issue number2
Publication statusPublished - 1 Apr 2018


  • Column sufficient tensor
  • H-eigenvalue
  • handicap
  • tensor complementarity problems

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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