A matrix version of the Wielandt inequality and its applications to statistics
文献类型：期刊论文
| 作者 | Wang, SG; Ip, WC |
| 刊名 | LINEAR ALGEBRA AND ITS APPLICATIONS
 |
| 出版日期 | 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 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000082618500010 |
| 出版者 | ELSEVIER SCIENCE INC |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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