On constrained generalized inverses of matrices and their properties

doi:10.1007/s10463-006-0075-3

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	On constrained generalized inverses of matrices and their properties
	Takane, Yoshio ; Tian, Yongge ; Yanai, Haruo
刊名	ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
	2007-12
卷号	59 期号:4 页码:807-820
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
ISSN号	0020-3157
DOI	10.1007/s10463-006-0075-3
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000251090800009
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/2581]
专题	上海财经大学
通讯作者	Takane, Yoshio
作者单位	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
推荐引用方式 GB/T 7714	Takane, Yoshio,Tian, Yongge,Yanai, Haruo. On constrained generalized inverses of matrices and their properties[J]. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS,2007,59(4):807-820.
APA	Takane, Yoshio,Tian, Yongge,&Yanai, Haruo.(2007).On constrained generalized inverses of matrices and their properties.ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS,59(4),807-820.
MLA	Takane, Yoshio,et al."On constrained generalized inverses of matrices and their properties".ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 59.4(2007):807-820.