ON THE GROUP INVERSE FOR THE SUM OF MATRICES

被引：3

作者：

Bu, Changjiang ^{[1
]}

Zhou, Xiuqing ^{[1
]}

Ma, Liang ^{[1
]}

Zhou, Jiang ^{[1
]}

机构：

[1] Harbin Engn Univ, Coll Sci, Harbin 150001, Peoples R China

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2014年 / 96卷 / 01期

基金：

美国国家科学基金会;

关键词：

group inverse; group invertibility; skew field; BLOCK MATRICES; DRAZIN-INVERSES; SKEW FIELDS;

D O I：

10.1017/S144678871300061X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K-mxn denote the set of all m x n matrices over a skew field K. In this paper, we give a necessary and sufficient condition for the existence of the group inverse of P + Q and its representation under the condition PQ = 0, where P, Q is an element of K-nxn. In addition, in view of the natural characters of block matrices, we give the existence and representation for the group inverse of P + Q and P + Q + R under some conditions, where P, Q, R is an element of K-nxn.

引用

页码：36 / 43

页数：8

共 50 条

[21] A weak group inverse for rectangular matrices
D. E. Ferreyra
V. Orquera
N. Thome
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019, 113 : 3727 - 3740
[22] The group inverse of some circulant matrices
Carmona, A.
Encinas, A. M.
Jimenez, M. J.
Mitjana, M.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 614 : 415 - 436
[23] A weak group inverse for rectangular matrices
Ferreyra, D. E.
Orquera, V.
Thome, N.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2019, 113 (04) : 3727 - 3740
[24] On group inverse of singular Toeplitz matrices
Wei, YM
Diao, H
LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 399 : 109 - 123
[25] Representations for the Drazin Inverse of the Sum of Two Matrices and its Applications
Li Guo
Jianlong Chen
Honglin Zou
Bulletin of the Iranian Mathematical Society, 2019, 45 : 683 - 699
[26] The least squares g-inverse for the sum of multiple matrices
Zheng, Yutao
Zheng, Bing
Xiong, Zhiping
APPLIED MATHEMATICS AND COMPUTATION, 2014, 231 : 591 - 600
[27] The Moore-Penrose inverse of a sum of three matrices - Solution
Neudecker, H
ECONOMETRIC THEORY, 1996, 12 (05) : 871 - 872
[28] The Generalized Inverse Inequalities for the Sum of Symmetric Nonnegative Definite Matrices
Ma, Ying
Wang, Shiqing
PROCEEDINGS OF 2010 3RD IEEE INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND INFORMATION TECHNOLOGY (ICCSIT 2010), VOL 8, 2010, : 572 - 575
[29] The Group Inverse of Some Block Matrices Composed by Idempotent Matrices
Fan, Zhaobin
Zheng, Jinshan
Bu, Changjiang
ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL 1: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS, 2008, : 40 - 43
[30] Representations for the Drazin Inverse of the Sum of Two Matrices and its Applications
Guo, Li
Chen, Jianlong
Zou, Honglin
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2019, 45 (03) : 683 - 699

← 1 2 3 4 5 →