华东师范大学学报（自然科学版） >

2023 , Vol. 2023 >Issue 4: 35 - 42

DOI: https://doi.org/10.3969/j.issn.1000-5641.2023.04.004

数学

{A,W}加权核-EP分解下的矩阵加权Drazin逆的刻画与表示

  • 胡春梅
展开
  • 丽江师范高等专科学校 数学与信息技术学院, 云南 丽江　674199
胡春梅, 女, 硕士, 讲师, 研究方向为矩阵和算子广义逆的理论及其应用.E-mail: chunmeihu2008@163.com

收稿日期: 2021-11-26

  网络出版日期: 2023-07-25

基金资助

云南省教育厅科学研究基金(2021J1149)

收起

Characterization and representation of weighted Drazin inverse of matrices based on weighted core-EP decomposition of the pair {A,W}

  • Chunmei HU
Expand
  • School of Mathematics and Information Technology, Lijiang Teachers College, Lijiang, Yunnan　674199, China

Received date: 2021-11-26

  Online published: 2023-07-25

Fold

摘要

主要讨论 $\{A, W\}$ 加权核-EP分解下的矩阵加权Drazin逆 $A^{d, W}$ . 将矩阵对 $\{A, W\}$ 进行核-EP分解, 得到 $A^{d, W}$ 的刻画, 进而推导出 $A^{d, W}$ 的表示. 最后讨论了 $A^{d, W}$ 的极限表示和积分表示, 并给出一个算例.

关键词： 加权Drazin逆; 加权核-EP分解; 极限表示; 积分表示

本文引用格式

胡春梅 . {A,W}加权核-EP分解下的矩阵加权Drazin逆的刻画与表示[J]. 华东师范大学学报（自然科学版）, 2023 , 2023(4) : 35 -42 . DOI: 10.3969/j.issn.1000-5641.2023.04.004

Abstract

This paper presents an investigation of the weighted Drazin inverse $A^{d, W}$ of matrices based on the weighted core-EP decomposition of the pair $\{A, W\}$ . Some characterizations and representations of the weighted Drazin inverse are presented using the weighted core-EP decomposition of the pair $\{A, W\}$ . Further, the limit representations and the integral representations of the weighted Drazin inverse are discussed. Furthermore, an example is presented.

Key words： weighted Drazin inverse; weighted core-EP decomposition; limit representation; integral representation

参考文献

1 ZHANG X Y, CHEN G L. The computation of Drazin inverse and its application in Markov chains. Applied Mathematics and Computation, 2006, 183, 292- 300.
1 . . 2006, 183, 292- 300.
2 CLINE R E, GREVILLE T N E. A Drazin inverse for rectangular matrices. Linear Algebra and its Applications, 1980, 29, 53- 62.
2 . . 1980, 29, 53- 62.
3 SHENG X P, CHEN G L. An oblique projection iterative method to compute Drazin inverse and group inverse. Applied Mathematics and Computation, 2009, 211, 417- 421.
3 . . 2009, 211, 417- 421.
4 CHEN Y L. Representation and approximation for the Drazin inverse $ A^{(d)} $ . Applied Mathematics and Computation, 2001, 119, 147- 160.
4 . . 2001, 119, 147- 160.
5 WANG H X. Core-EP decomposition and its applications. Linear Algebra and its Application, 2016, 508, 289- 300.
5 . . 2016, 508, 289- 300.
6 FERREYRA D E, LEVIS F E, THOME N. Revisiting the core EP inverse and its extension to rectangular matrices. Quaestiones Mathematicae, 2018, 41, 265- 281.
6 . . 2018, 41, 265- 281.
7 FERREYRA D E, ORQUERA V, THOME N. A weak group inverse for rectangular matrices. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019, 113, 3727- 3740.
7 . . 2019, 113, 3727- 3740.
8 WANG G R, WEI Y M, QIAO S Z. Generalized Inverses: Theory and Computations [M]. Beijing: Science Press, 2004: 52-64.
9 WEI Y M, DJORDJEVI? D S. On integral representation of the generalized inverse $ A^{(2)}_{T, S} $ . Applied Mathematics and Computation, 2003, 142, 189- 194.
9 . . 2003, 142, 189- 194.
Options
文章导航

/

〈 〉