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
收藏
页码：818 / 833
页数：16
相关论文
共 50 条
  • [41] A note on "5 x 5 Completely positive matrices"
    Dong, Hongbo
    Anstreicher, Kurt
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 433 (05) : 1001 - 1004
  • [42] Symmetric perimeters of completely positive Boolean matrices and their preservers
    Kang, Kyung-Tae
    Song, Seok-Zun
    Jun, Young Bae
    LINEAR & MULTILINEAR ALGEBRA, 2025,
  • [43] The Cone of 5 x 5 Completely Positive Matrices
    Pfeffer, Max
    Samper, Jose Alejandro
    DISCRETE & COMPUTATIONAL GEOMETRY, 2024, 71 (02) : 442 - 466
  • [44] Triangle-free graphs and completely positive matrices
    Abraham Berman
    Naomi Shaked-Monderer
    Central European Journal of Operations Research, 2022, 30 : 1093 - 1099
  • [45] Chains of dog-ears for completely positive matrices
    Barioli, F
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 330 (1-3) : 49 - 66
  • [46] OPEN PROBLEMS IN THE THEORY OF COMPLETELY POSITIVE AND COPOSITIVE MATRICES
    Berman, Abraham
    Duer, Mirjam
    Shaked-Monerer, Naomi
    ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2015, 29 : 46 - 58
  • [47] Triangle-free graphs and completely positive matrices
    Berman, Abraham
    Shaked-Monderer, Naomi
    CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH, 2022, 30 (03) : 1093 - 1099
  • [48] CP rank of completely positive matrices of order 5
    Loewy, R
    Tam, BS
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 363 : 161 - 176
  • [49] COMPLETELY O-SIMPLE SEMIRINGS
    GRILLET, MP
    GRILLET, PA
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 155 (01) : 19 - &
  • [50] Congruences on quasi completely regular semirings
    S. K. Maity
    R. Ghosh
    Semigroup Forum, 2021, 102 : 725 - 736
12345