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

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