Some further matrix extensions of the Cauchy-Schwarz and Kantorovich inequalities, with some statistical applications

被引：21

作者：

Pecaric, JE

Puntanen, S

Styan, GPH

机构：

[1] UNIV TAMPERE,DEPT MATH SCI,FIN-33101 TAMPERE,FINLAND

[2] MCGILL UNIV,DEPT MATH & STAT,MONTREAL,PQ H3A 2K6,CANADA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1996年 / 237卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

D O I：

10.1016/0024-3795(95)00679-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The well-known Cauchy-Schwarz and Kantorovich inequalities may be expressed in terms of vectors and a positive definite matrix. We consider what happens to these inequalities when the vectors are replaced by matrices, the positive definite matrix is allowed to be positive semidefinite singular, and the usual inequalities are replaced by Lowner partial orderings. Some examples in the context of linear statistical models are presented.

引用

页码：455 / 476

页数：22

共 42 条

[1]

[Anonymous], 1994, LINEAR MULTILINEAR A, DOI [DOI 10.1080/03081089408818291, 10.1080/03081089408818291]

[2]

[Anonymous], 1990, AEQUATIONES MATH, DOI DOI 10.1007/BF02112284

[3]

Baksalary J.K., 1980, B ACAD POL SCI SMAP, V28, P233

[4] CHARACTERIZATIONS OF THE BEST LINEAR UNBIASED ESTIMATOR IN THE GENERAL GAUSS-MARKOV MODEL WITH THE USE OF MATRIX PARTIAL ORDERINGS [J].