KMS Of Academy of mathematics and systems sciences, CAS
A matrix version of the Wielandt inequality and its application to statistics | |
Wang, SG; Ip, WC | |
1999 | |
Source Publication | CHINESE SCIENCE BULLETIN |
ISSN | 1001-6538 |
Volume | 44Issue:2Pages:118-121 |
Abstract | 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. |
Keyword | Wielandt inequality Cauchy-Schwarz inequality Wishart matrix |
Language | 英语 |
WOS Research Area | Science & Technology - Other Topics |
WOS Subject | Multidisciplinary Sciences |
WOS ID | WOS:000079243000006 |
Publisher | SCIENCE PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/14532 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | 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 |
Recommended Citation 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. |
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