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A matrix version of the Wielandt inequality and its application to statistics
Wang, SG; Ip, WC
1999
Source PublicationCHINESE SCIENCE BULLETIN
ISSN1001-6538
Volume44Issue:2Pages:118-121
AbstractSuppose 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.
KeywordWielandt inequality Cauchy-Schwarz inequality Wishart matrix
Language英语
WOS Research AreaScience & Technology - Other Topics
WOS SubjectMultidisciplinary Sciences
WOS IDWOS:000079243000006
PublisherSCIENCE PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/14532
Collection中国科学院数学与系统科学研究院
Affiliation1.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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