Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications

被引：19

作者：

Wang, Qingwen ^{[1
]}

Song, Guangjing ^{[1
]}

Liu, Xin ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

ALGEBRA COLLOQUIUM | 2009年 / 16卷 / 02期

关键词：

system of matrix equations; division ring; maximal rank; minimal rank; generalized inverses; EXPRESSION SUBJECT; REGULAR-RINGS; SYSTEM; PAIR;

D O I：

10.1142/S1005386709000297

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the formulas of the maximal and minimal ranks of the common solution of certain linear matrix equations A(1)X = C-1, X B-2 = C-2, A(3)XB(3) = C-3 and A(4)X B-4 = C-4 over an arbitrary division ring. Corresponding results in some special cases are given. As an application, necessary and sufficient conditions for the invariance of the rank of the common solution mentioned above are presented. Some previously known results can be regarded as special cases of our results.

引用

页码：293 / 308

页数：16

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