On {0,1} CP tensors and CP pseudographs

Changqing Xu, Zhibing Chen, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

Abstract

A positive semidefinite matrix can be written as a Gramian matrix, and a completely positive matrix can therefore be written as a Gramian matrix of some nonnegative vectors. In this paper, we introduce Gramian tensors and study 2-dimension completely positive tensors and {0,1}−CP tensors. Also investigated are the complete positive multi-hypergraph which are a generalized form of cp graphs. We also provide a necessary and sufficient condition for a 2-dimensional tensor to be completely positive.

Original languageEnglish
Pages (from-to)287-306
Number of pages20
JournalLinear Algebra and Its Applications
Volume557
DOIs
Publication statusPublished - 15 Nov 2018

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

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