Explicit formulas for determinantal representations of the Drazin inverse solutions of some matrix and differential matrix equations

被引：26

作者：

Kyrchei, Ivan ^{[1
]}

机构：

[1] NAS Ukraine, Pidstrygach Inst Appl Problems Mech & Math, UA-79060 Lvov, Ukraine

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 219卷 / 14期

关键词：

Drazin inverse; Matrix equation; Drazin inverse solution; Cramer rule; Differential matrix equation; LEAST-SQUARES SOLUTIONS; CRAMER RULE;

D O I：

10.1016/j.amc.2013.01.050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Drazin inverse solutions of the matrix equations AX = B, XA = B and AXB = D are considered in this paper. We use both the determinantal representations of the Drazin inverse obtained earlier by the author and in the paper. We get analogs of the Cramer rule for the Drazin inverse solutions of these matrix equations and using their for determinantal representations of solutions of some differential matrix equations, X' + AX = B and X' + XA = B, where the matrix A is singular. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：7632 / 7644

页数：13

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