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

共 16 条

[11]

Tian Y., 2003, NEW YORK J MATH, V9, P345

[12]

Tian Y., 2002, SEA B MATH, V25, P745, DOI [10.1007/s100120200015, DOI 10.1007/S100120200015]

[13] Upper and lower bounds for ranks of matrix expressions using generalized inverses [J].

Tian, YG .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 355 :187-214

[14] On common generalized inverses of a pair of matrices [J].

Tian, YG ;

Takane, Y .

LINEAR & MULTILINEAR ALGEBRA, 2006, 54 (03) :195-209

[15] More on maximal and minimal ranks of Schur complements with applications [J].

Tian, YG .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 152 (03) :675-692

[16] SOME GENERALIZED FORMS OF LEAST-SQUARES G-INVERSE, MINIMUM NORM G-INVERSE, AND MOORE-PENROSE INVERSE MATRICES [J].

YANAI, H .

COMPUTATIONAL STATISTICS & DATA ANALYSIS, 1990, 10 (03) :251-260

← 1 2 →