On constrained generalized inverses of matrices and their properties

被引：0
作者：
Yoshio Takane
Yongge Tian
Haruo Yanai
机构：
[1] McGill University,Department of Psychology
[2] Shanghai University of Finance and Economics,School of Economics
[3] St. Luke’s College of Nursing,undefined
来源：
Annals of the Institute of Statistical Mathematics | 2007年 / 59卷
关键词：
Linear matrix expression; Moore–Penrose inverse; Constrained generalized inverses; Matrix equation; Projector; Idempotent matrix; Rank equalities; General linear model; Weighted least-squares estimator;
D O I：
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中图分类号：
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摘要：
A matrix G is called a generalized inverse (g-invserse) of matrix A if AGA  =  A and is denoted by G  = A−. Constrained g-inverses of A are defined through some matrix expressions like E(AE)−, (FA)−F and E(FAE)−F. In this paper, we derive a variety of properties of these constrained g-inverses by making use of the matrix rank method. As applications, we give some results on g-inverses of block matrices, and weighted least-squares estimators for the general linear model.
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页码：807 / 820
页数：13
相关论文
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