Properties of Some Classes of Structured Tensors

Yisheng Song, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

117 Citations (Scopus)


In this paper, we extend some classes of structured matrices to higher-order tensors. We discuss their relationships with positive semi-definite tensors and some other structured tensors. We show that every principal sub-tensor of such a structured tensor is still a structured tensor in the same class, with a lower dimension. The potential links of such structured tensors with optimization, nonlinear equations, nonlinear complementarity problems, variational inequalities and the non-negative tensor theory are also discussed.
Original languageEnglish
Pages (from-to)854-873
Number of pages20
JournalJournal of Optimization Theory and Applications
Issue number3
Publication statusPublished - 1 Jun 2015


  • (formula presented)
  • B tensor
  • Eigenvalues
  • P tensor
  • Principal sub-tensor

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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