On {0,1} CP tensors and CP pseudographs

Changqing Xu; Zhibing Chen; Liqun Qi

doi:10.1016/j.laa.2018.08.001

On {0,1} CP tensors and CP pseudographs

Changqing Xu
, Zhibing Chen
, Liqun Qi

Research output: Journal article publication › Journal article › Academic research › peer-review

2 Citations (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 language	English
Pages (from-to)	287-306
Number of pages	20
Journal	Linear Algebra and Its Applications
Volume	557
DOIs	https://doi.org/10.1016/j.laa.2018.08.001
Publication status	Published - 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

More information

10.1016/j.laa.2018.08.001

Cite this

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AU - Xu, Changqing

AU - Chen, Zhibing

AU - Qi, Liqun

PY - 2018/11/15

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N2 - 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.

AB - 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.

KW - (0,1) tensor

KW - Completely positive tensor

KW - Multi-hypergraph

KW - {0,1} completely positive tensor

UR - https://www.scopus.com/pages/publications/85051022743

U2 - 10.1016/j.laa.2018.08.001

DO - 10.1016/j.laa.2018.08.001

M3 - Journal article

AN - SCOPUS:85051022743

SN - 0024-3795

VL - 557

SP - 287

EP - 306

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

On {0,1} CP tensors and CP pseudographs

Abstract

Keywords

ASJC Scopus subject areas

More information

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