非负矩阵的核单调刻画

兰州理工大学学报 ›› 2025, Vol. 51 ›› Issue (3): 167-172.

• 数理科学 • 上一篇

非负矩阵的核单调刻画

林麟¹, 钟金^*2

1.南昌交通学院基础学科部, 江西南昌 330100;
2.江西理工大学理学院, 江西赣州 341000

收稿日期:2023-05-10 出版日期:2025-06-28 发布日期:2025-06-30
作者简介:钟金(1984-),男,江西赣州人,博士,副教授.Email:zhongjin1984@126.com
基金资助:
国家自然科学基金(12261043)

Core-monotonicity characterizations for nonnegative matrices

LIN Lin¹, ZHONG Jin²

1. Department of Basic Courses, Nanchang Jiaotong Institute, Nanchang 330100, China;
2. Faculty of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China

Received:2023-05-10 Online:2025-06-28 Published:2025-06-30

摘要/Abstract

摘要： 研究了非负矩阵核单调的刻画问题.利用非负满秩分解给出了非负矩阵是核单调的充分必要条件,并给出了核逆非负时的表示.通过数值例子说明了非负矩阵的核逆与Moore-Penrose逆和群逆的非负性不是等价的,并利用矩阵的Moore-Penrose逆和群逆给出了非负矩阵是核单调的一个充分必要条件.此外,给出了一个实矩阵是核单调的充分必要条件,推广了Collatz的结果.

关键词: 非负矩阵, 核逆, 核单调, 对偶核单调

Abstract: Characterizations for the core-monotonicity of nonnegative matrices are studied. A sufficient and necessary condition for core-monotonicity of nonnegative matrices is presented by nonnegative full-rank decomposition, and the representation of the core inverse is also given when it is nonnegative. It is shown by some numerical examples that the nonnegativity of the core inverse and the Moore-Penrose is not equivalent to the group inverse of nonnegative matrices. Furthermore, a sufficient and necessary condition for the core-monotonicity of nonnegative matrices is given by using the Moore-Penrose inverse and group inverse. Additionally, a sufficient and necessary condition for the core-monotonicity of real matrices is presented, which extends the results of Collatz.

Key words: nonnegative matrix, core inverse, core-monotonicity, dual core-monotonicity

中图分类号:

O151.21

林麟, 钟金. 非负矩阵的核单调刻画[J]. 兰州理工大学学报, 2025, 51(3): 167-172.

LIN Lin, ZHONG Jin. Core-monotonicity characterizations for nonnegative matrices[J]. Journal of Lanzhou University of Technology, 2025, 51(3): 167-172.

参考文献

[1] COLLATZ L.Aufgaben monotoner art[J].Archiv der Matematik,1952,3(5):366-376.
[2] COLLATZ L.Functional analysis and numerical mathematics[M].New York:Academic,1966.
[3] MANGASARIAN O L.Characterization of real matrices of monotone kind[J].SIAM Review,1968,10(4):439-441.
[4] BERMAN A,PLEMMONS R J.Nonnegative matrices in the mathematical sciences[M].Philadelphia:Society for Industrial and Applied Mathematics,1994.
[5] PLEMMONS R J,CLINE R E.The generalized inverse of a nonnegative matrix[J].Proceedings of the American Mathematical Society,1972,31(1):46-50.
[6] JAIN S K,KWAK E K,GOEL V K.Decomposition of nonnegative group-monotone matrices[J].Transactions of the American Mathematical Society,1980,257(2):371-385.
[7] PYE W C.Nonnegative drazin inverses[J].Linear Algebra and Its Applications,1980,30:149-153.
[8] MISHRA D,SIVAKUMAR K C.Nonnegative generalized inverses and least elements of polyhedral sets[J].Linear Algebra and Its Applications,2011,434(12):2448-2455.
[9] JENA L,PANI S.Interval drazin monotonicity of matrices[J].Vietnam J Math,2013,41(3):313-321.
[10] SIVAKUMAR K C.Nonnegative generalized inverses and certain subclasses of singular Q-matrices[J].Linear Algebra and Its Applications,2013,438(12):4701-4708.
[11] BAKSALARY O M,TRENKLER G.Core inverse of matrices[J].Linear Multilinear Algebra,2010,58(6):681-697.
[12] 张之月,马海凤.张量积下核逆的扰动界[J].高等学校计算数学学报,2021,43(3):267-291.
[13] 李开玲,杜法鹏.三角分块矩阵的核逆的表示[J].高等学校计算数学学报,2020,42(3):209-218.
[14] MA H.Optimal perturbation bounds for the core inverse[J].Applied Mathematics and Computation,2018,336:176-181.
[15] WANG H,LIU X.Characterizations of the core inverse and the core partial orderings[J].Applied Mathematics and Computation,2015,63(9):1829-1836.
[16] LI T,CHEN J.Characterizations of core and dual core inverse in rings with involution[J].Linear and Multilinear Algebra,2018,66(4):717-730.
[17] CHEN J,ZHU H,PATRICIO P,et al.Characterizations and representations of the core and dual core inverse[J].Canadian Mathematical Bulletin,2016,60(2):1-19.
[18] WANG G,WEI Y,QIAO S.Generalized inverses:theory and computation[M].Singapore:Springer,2018.
[19] 詹兴致.矩阵论[M].北京: 高等教育出版社,2008.
[20] RAKIĆD S, DINČIĆ N Č,DJORDJEVIĆ D S.Group,Moore-Penrose,core and dual core inverse in rings with involution[J].Linear Algebra and Its Applications,2014,463:115-133.
[21] FLOR P.On groups of nonnegative matrices[J].Compositio Mathematica,1969,21:376-382.

非负矩阵的核单调刻画

Core-monotonicity characterizations for nonnegative matrices

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价