KMS Of Academy of mathematics and systems sciences, CAS
A matrix version of the Wielandt inequality and its applications to statistics | |
Wang, SG; Ip, WC | |
1999-07-15 | |
Source Publication | LINEAR ALGEBRA AND ITS APPLICATIONS |
ISSN | 0024-3795 |
Volume | 296Issue:1-3Pages:171-181 |
Abstract | 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 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. |
Keyword | Wielandt inequality Kantorovich inequality Cauchy-Schwarz inequality canonical correlation condition number generalized inverse |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000082618500010 |
Publisher | ELSEVIER SCIENCE INC |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/14340 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | 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 |
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. |
Files in This Item: | ||||||
There are no files associated with this item. |
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment