On minimal solutions of the matrix equation AX-YB=0

被引：7

作者：

Dobovisek, M ^{[1
]}

机构：

[1] Univ Ljubljana, Dept Math, Ljubljana 1000, Slovenia

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2001年 / 325卷 / 1-3期

关键词：

D O I：

10.1016/S0024-3795(00)00294-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the case when one of the ranks of matrices A or B is full, all self-adjoint pairs of solutions of the equation AX - YB = 0 are given. Necessary and sufficient conditions for the existence of nonnegative and positive definite solutions are proved. Without any condition on ranks and with a given solution X, it is shown that maximal and minimal solutions for Y do not exist in nontrivial cases. It is also proved that the minimal nonnegative solution Y exists. An explicit formula for this solution is given. (C) 2001 Elsevier Science Inc. All rights reserved.

引用

页码：81 / 99

页数：19

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