CAUCHY-SCHWARZ INEQUALITIES ASSOCIATED WITH POSITIVE SEMIDEFINITE MATRICES

被引：60

作者：

HORN, RA ^{[1
]}

MATHIAS, R ^{[1
]}

机构：

[1] JOHNS HOPKINS UNIV,DEPT MATH SCI,BALTIMORE,MD 21218

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1990年 / 142卷

关键词：

D O I：

10.1016/0024-3795(90)90256-C

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using a quasilinear representation for unitarily invariant norms, we prove a basic inequality: Let A= L X X* M be positive semidefinite, where X∈Mm,n. Then |||X|p||2≤{norm of matrix}Lp{norm of matrix} {norm of matrix}Mp{norm of matrix} for all p>0 and all unitarily invariant norms {norm of matrix}·{norm of matrix}. We show how several inequalities of Cauchy-schwarz type follow from this bound and obtain a partial analog of our results for lp norms. © 1990.

引用

页码：63 / 82

页数：20

共 22 条

[1] CONCAVITY OF CERTAIN MAPS ON POSITIVE DEFINITE MATRICES AND APPLICATIONS TO HADAMARD PRODUCTS [J].