Orderings on semirings and completely positive matrices

被引：3

作者：

Mohindru, Preeti ^{[1
]}

Pereira, Rajesh ^{[1
]}

机构：

[1] Univ Guelph, Dept Math & Stat, Guelph, ON N1G 2W1, Canada

来源：

LINEAR & MULTILINEAR ALGEBRA | 2016年 / 64卷 / 05期

基金：

加拿大自然科学与工程研究理事会;

关键词：

matrices over semirings; completely positive matrices; diagonally dominant matrices; inclines; ordered semirings; 15B33; 15B48; 06A75; 16Y60; NONNEGATIVE FACTORIZATION;

D O I：

10.1080/03081087.2015.1059405

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A real symmetric matrix is called a completely positive matrix if there exists a nonnegative real matrix such that. In this paper, we extend the notion of complete positivity for matrices over real numbers to matrices over semirings in general. We find necessary and sufficient conditions for matrices over certain semirings to be completely positive. We also find an upper bound on the CP-rank of completely positive matrices over certain special types of semirings.

引用

页码：818 / 833

页数：16

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