On constrained generalized inverses of matrices and their properties

被引：6

作者：

Takane, Yoshio

Tian, Yongge

Yanai, Haruo

机构：

[1] McGill Univ, Dept Psychol, Montreal, PQ H3A 1B1, Canada

[2] Shanghai Univ Finance & Econ, Sch Econ, Shanghai 200433, Peoples R China

[3] St Lukes Coll Nursing, Chuo Ku, Tokyo, Japan

来源：

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 2007年 / 59卷 / 04期

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：

10.1007/s10463-006-0075-3

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：807 / 820

页数：14

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