CAUCHY-SCHWARZ INEQUALITIES ASSOCIATED WITH POSITIVE SEMIDEFINITE MATRICES

被引：58
|
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.
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收藏
页码：63 / 82
页数：20
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