{0,1} completely positive tensors and multi-hypergraphs

Changqing Xu, Ziyan Luo, Liqun Qi, Zhibing Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)

Abstract

Completely positive graphs have been employed to associate with completely positive matrices for characterizing the intrinsic zero patterns. As tensors have been widely recognized as a higher-order extension of matrices, the multi-hypergraph, regarded as a generalization of graphs, is then introduced to associate with tensors for the study of complete positivity. To describe the dependence of the corresponding zero pattern for a special type of completely positive tensors—the {0,1} completely positive tensors, the completely positive multi-hypergraph is defined. By characterizing properties of the associated multi-hypergraph, we provide necessary and sufficient conditions for any (0,1) associated tensor to be {0,1} completely positive. Furthermore, a necessary and sufficient condition for a uniform multi-hypergraph to be a completely positive multi-hypergraph is proposed as well.
Original languageEnglish
Pages (from-to)110-123
Number of pages14
JournalLinear Algebra and Its Applications
Volume510
DOIs
Publication statusPublished - 1 Dec 2016

Keywords

  • (0,1) tensor
  • Completely positive tensor
  • Multi-hypergraph
  • {0,1} completely positive tensor

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

Cite this