Some properties of submatrices in a solution to the matrix equation AXB = C with applications

被引：13

作者：

Tian, Yongge ^{[1
]}

机构：

[1] Cent Univ Finance & Econ, China Econ & Management Acad, Beijing, Peoples R China

来源：

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2009年 / 346卷 / 06期

关键词：

Generalized inverse; Independence of solutions; Rank formulas; Maximal and minimal ranks; Linear matrix equations; General solutions; Submatrices; RANK EQUALITIES; BLOCK MATRICES;

D O I：

10.1016/j.jfranklin.2009.02.013

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Suppose that AXB = C is a consistent matrix equation and partition its solution X into a 2 x 2 block form. In this article we give some formulas for the maximal and minimal ranks of the submatrices in a solution X to AXB = C. From these formulas, we derive necessary and sufficient conditions for the submatrices to be zero and nonsingular, respectively. As applications, we give a group of formulas for the maximal and minimal ranks of submatrices in generalized inverses of matrices and their properties. (C) 2009 Published by Elsevier Ltd. on behalf of The Franklin Institute.

引用

页码：557 / 569

页数：13

共 50 条

[41] The (P,Q) reflexive solutions of the matrix equation AXB = C
Zhang, Jianchen
Zhou, Shuzi
Hu, Xiyan
PROCEEDINGS OF THE THIRD INTERNATIONAL WORKSHOP ON MATRIX ANALYSIS AND APPLICATIONS, VOL 3, 2009, : 200 - 204
[42] Global-DGMRES method for matrix equation AXB = C
Safarzadeh, Malihe
Sadeghi Goughery, Hossein
Salemi, Abbas
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2022, 99 (05) : 1005 - 1021
[43] The solution of the matrix equation AXB = D and the system of matrix equations AX = C, XB = D with X *X = Ip
Zhang, Huiting
Liu, Lina
Liu, Hao
Yuan, Yongxin
APPLIED MATHEMATICS AND COMPUTATION, 2022, 418
[44] New matrix iterative methods for constraint solutions of the matrix equation AXB = C
Peng, Zhen-yun
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 235 (03) : 726 - 735
[45] The　Metapositive　Definite　Self－Conjugate　Solution　of　the　Matrix　Equation　AXB＝C　over　a　Skew　Field
王卿文
Chinese Quarterly Journal of Mathematics, 1995, (03) : 42 - 51
[46] Least-squares solution with the minimum-norm for the matrix equation (AXB, GXH) = (C, D)
Liao, AP
Lei, Y
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 50 (3-4) : 539 - 549
[47] MAXIMUM AND MINIMUM RANKS AND INERTIAS OF THE HERMITIAN PARTS OF THE LEAST RANK SOLUTION OF THE MATRIX EQUATION AXB = C
Guerarra, Sihem
NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION, 2021, 11 (01): : 75 - 86
[48] Some remarks on Jacobi and Gauss-Seidel-type iteration methods for the matrix equation AXB = C
Liu, Zhongyun
Zhou, Yang
Zhang, Yuelan
Lin, Lu
Xie, Dongxiu
APPLIED MATHEMATICS AND COMPUTATION, 2019, 354 : 305 - 307
[49] THE MATRIX EQUATION AXB + CYD=E
BAKSALARY, JK
KALA, R
LINEAR ALGEBRA AND ITS APPLICATIONS, 1980, 30 (APR) : 141 - 147
[50] An Efficient Algorithm for the Reflexive Solution of the Quaternion Matrix Equation AXB + CXHD = F
Li, Ning
Wang, Qing-Wen
Jiang, Jing
JOURNAL OF APPLIED MATHEMATICS, 2013,

← 1 2 3 4 5 →