A matrix version of the Wielandt inequality and its applications to statistics

	A matrix version of the Wielandt inequality and its applications to statistics
	Wang, SG ; Ip, WC
刊名	LINEAR ALGEBRA AND ITS APPLICATIONS
	1999-07-15
卷号	296 期号:1-3 页码:171-181
关键词	Wielandt inequality Kantorovich inequality Cauchy-Schwarz inequality canonical correlation condition number generalized inverse
ISSN号	0024-3795
英文摘要	Suppose that A is an n x n positive definite Hermitian matrix. Let X and Y be n x p and n x q matrices, respectively, such that XY = 0. The present article proves the following inequality, XAY(YAY)Y-AX less than or equal to (lambda(1)-lambda(n)/lambda(1)+lambda(n))X-2*AX, where lambda(1) and lambda(n) are respectively the largest and smallest eigenvalues of A, and M- stands for a generalized inverse of M. This inequality is an extension of the well-known Wielandt inequality in which both X and Y are vectors. The inequality is utilized to obtain some interesting inequalities about covariance matrix and various correlation coefficients including the canonical correlation, multiple and simple correlations. Some applications in parameter estimation are also given. (C) 1999 Elsevier Science Inc. All rights reserved.
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER SCIENCE INC
WOS记录号	WOS:000082618500010
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/14339]
专题	中国科学院数学与系统科学研究院
通讯作者	Ip, WC
作者单位	1.Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong 2.Beijing Polytech Univ, Dept Appl Math, Beijing 100022, Peoples R China 3.Acad Sinica, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Wang, SG,Ip, WC. A matrix version of the Wielandt inequality and its applications to statistics[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,1999,296(1-3):171-181.
APA	Wang, SG,&Ip, WC.(1999).A matrix version of the Wielandt inequality and its applications to statistics.LINEAR ALGEBRA AND ITS APPLICATIONS,296(1-3),171-181.
MLA	Wang, SG,et al."A matrix version of the Wielandt inequality and its applications to statistics".LINEAR ALGEBRA AND ITS APPLICATIONS 296.1-3(1999):171-181.