Upper and lower bounds for ranks of matrix expressions using generalized inverses

被引：101
|
作者：
Tian, YG [1 ]
机构：
[1] Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2002年 / 355卷
基金：
加拿大自然科学与工程研究理事会;
关键词：
generalized inverse; invariance; matrix equation; matrix expression; range; rank; Schur complement;
D O I：
10.1016/S0024-3795(02)00345-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The maximal and minimal ranks of the matrix expression A(1) - B1X1C1 - B2X2C2 with respect to X-1 and X-2 are presented. As applications, the maximal and minimal ranks of A(1) - B1XC1 subject to a consistent matrix equation B2XC2 = A(2) are also determined. In addition, the maximal and minimal ranks of the Schur complement D - CA(-)B with respect to the generalized inverse A(-) of A and their various consequences are also considered. (C) 2002 Elsevier Science Inc. All rights reserved.
引用
收藏
页码：187 / 214
页数：28
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