Cauchy不等式矩阵形式的推广  

Generalizations of Cauchy inequality about matrix versions

作　　者：程伟丽[1] 齐静[2] 

机构地区：[1]华北水利水电学院数学与信息科学学院,河南郑州450011 [2]郑州轻工业学院数学与信息科学系,河南郑州450002

出　　处：《郑州轻工业学院学报（自然科学版）》2008年第4期118-120,共3页Journal of Zhengzhou University of Light Industry:Natural Science

基　　金：河南省自然科学基金项目(0611052600)

摘　　要：设A为n×n正定Hermite阵,x为n维列向量,得到了Cauchy不等式的推广形式,进一步设A为n×n半正定Hermite阵,若x∈μ(A),推广形式仍成立.将向量x为n维列向量推广为X为n×p矩阵,且满足X*X=Ip,则有进一步推广.Let A be an n×n positive definite Hermite matrix,x be a vector of dimension n, the generalized Cauchy inequality is obtained. And more, let A be an n×n semi-positive definite Hermite matrix and x ∈μ （A）, the inequality is established also. Thirdly, let X is n×p real matrix and is X^＊X =Ip, the generalized Cauchy inequality is obtained.

关 键 词：CAUCHY不等式 矩阵形式 平均值不等式 

分 类 号：O151.21[理学—数学]