Primitive tensors and directed hypergraphs

Lu Bin Cui; Wen Li; Kwok Po NG

doi:10.1016/j.laa.2014.12.033

Primitive tensors and directed hypergraphs

Lu Bin Cui, Wen Li^*, Kwok Po NG

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

Primitivity is an important concept in the spectral theory of nonnegative matrices and tensors. It is well-known that an irreducible matrix is primitive if and only if the greatest common divisor of all the cycles in the associated directed graph is equal to 1. The main aim of this paper is to establish a similar result, i.e., we show that a nonnegative tensor is primitive if and only if the greatest common divisor of all the cycles in the associated directed hypergraph is equal to 1.

Original language	English
Pages (from-to)	96-108
Number of pages	13
Journal	Linear Algebra and Its Applications
Volume	471
DOIs	https://doi.org/10.1016/j.laa.2014.12.033
Publication status	Published - 15 Apr 2015

Scopus Subject Areas

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

User-Defined Keywords

Directed hypergraph
Irreducible tensor
Nonnegative tensor
Primitive tensor

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10.1016/j.laa.2014.12.033

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AU - NG, Kwok Po

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N2 - Primitivity is an important concept in the spectral theory of nonnegative matrices and tensors. It is well-known that an irreducible matrix is primitive if and only if the greatest common divisor of all the cycles in the associated directed graph is equal to 1. The main aim of this paper is to establish a similar result, i.e., we show that a nonnegative tensor is primitive if and only if the greatest common divisor of all the cycles in the associated directed hypergraph is equal to 1.

AB - Primitivity is an important concept in the spectral theory of nonnegative matrices and tensors. It is well-known that an irreducible matrix is primitive if and only if the greatest common divisor of all the cycles in the associated directed graph is equal to 1. The main aim of this paper is to establish a similar result, i.e., we show that a nonnegative tensor is primitive if and only if the greatest common divisor of all the cycles in the associated directed hypergraph is equal to 1.

KW - Directed hypergraph

KW - Irreducible tensor

KW - Nonnegative tensor

KW - Primitive tensor

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JO - Linear Algebra and Its Applications

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Primitive tensors and directed hypergraphs

Abstract

Scopus Subject Areas

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