MP弱Core逆的性质和应用

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1619-1632.

MP弱Core逆的性质和应用

刘晓冀(),廖梦月(),靳宏伟*()

^{广西民族大学数学与物理学院南宁 530006}

收稿日期:2021-12-03 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 靳宏伟 E-mail:xiaojiliu72@126.com;zashmy@163.com;jhw_math@126.com
作者简介:刘晓冀, E-mail: xiaojiliu72@126.com|廖梦月, E-mail: zashmy@163.com
基金资助:
国家自然科学基金(12061015);广西自然科学基金(2018GXNSFDA281023);广西科技基地与人才专项基金(桂科AD21220024)

The Properties and Applications of the MP Weak Core Inverse

Xiaoji Liu(),Mengyue Liao(),Hongwei Jin*()

^{School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006}

Received:2021-12-03 Online:2022-12-26 Published:2022-12-16
Contact: Hongwei Jin E-mail:xiaojiliu72@126.com;zashmy@163.com;jhw_math@126.com
Supported by:
the National Natural Science Foundation of China(12061015);the Guangxi Natural Science Foundation(2018GXNSFDA281023);the Special Fund for Science and Technological Bases and Talents of Guangxi(桂科AD21220024)

摘要/Abstract

摘要：

基于Moore-Penrose逆和弱Core逆该文提出了Moore-Penrose弱Core逆(MPWC逆)的概念.分别从代数和几何角度对它进行刻画, 给出了MPWC逆与非奇异加边矩阵之间的关系, 应用Hartwig-Spindelböck分解和Core-EP分解给出了MPWC逆的性质、刻画及其扰动分析, 最后给出了矩阵的MPWC逆是EP矩阵的等价条件

关键词: 弱Core逆, Moore-Penrose逆, MPWC逆, Core-EP分解

Abstract:

In this paper, the concept of the Moore-Penrose weak Core inverse (MPWC inverse) is proposed based on the Moore-Penrose inverse and the weak Core inverse. It is described from algebraic and geometric perspectives respectively. The relationship between the MP weak Core inverse and the nonsingular bordered matrix is given. The expression of the MP weak Core inverse is given by using the Hartwig-Spindelböck decomposition and the Core-EP decomposition. The equivalence between the MP weak Core inverse of a matrix and EP matrix, the characterization and the perturbation analysis are given.

Key words: Weak Core inverse, Moore-Penrose inverse, MPWC inverse, Core-EP decomposition

中图分类号:

O151

刘晓冀,廖梦月,靳宏伟. MP弱Core逆的性质和应用[J]. 数学物理学报, 2022, 42(6): 1619-1632.

Xiaoji Liu,Mengyue Liao,Hongwei Jin. The Properties and Applications of the MP Weak Core Inverse[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1619-1632.

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