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

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	A matrix version of the Wielandt inequality and its application to statistics
	Wang, SG ; Ip, WC
	1999
发表期刊	CHINESE SCIENCE BULLETIN
ISSN	1001-6538
卷号	44 期号:2 页码:118-121
摘要	Suppose that A is an n (x) n positive definite Hemitain matrix. Let X and Y be n (x) p and n (x) q matrices (p + q less than or equal to n), such that X* Y = 0, the following inequality is proved [GRAPHICS] where lambda(t) 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 correlation.
关键词	Wielandt inequality Cauchy-Schwarz inequality Wishart matrix
语种	英语
WOS研究方向	Science & Technology - Other Topics
WOS类目	Multidisciplinary Sciences
WOS记录号	WOS:000079243000006
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/14532
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, SG
作者单位	1.Beijing Polytech Univ, Dept Appl Math, Beijing 100022, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China 3.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, 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 application to statistics[J]. CHINESE SCIENCE BULLETIN,1999,44(2):118-121.
APA	Wang, SG,&Ip, WC.(1999).A matrix version of the Wielandt inequality and its application to statistics.CHINESE SCIENCE BULLETIN,44(2),118-121.
MLA	Wang, SG,et al."A matrix version of the Wielandt inequality and its application to statistics".CHINESE SCIENCE BULLETIN 44.2(1999):118-121.