A matrix version of the Wielandt inequality and its applications to statistics
Wang, SG; Ip, WC
AbstractSuppose 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 X*Y = 0. The present article proves the following inequality, X*AY(Y*AY)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.
KeywordWielandt inequality Kantorovich inequality Cauchy-Schwarz inequality canonical correlation condition number generalized inverse
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000082618500010
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Cited Times:21[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Affiliation1.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
Recommended Citation
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.
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