非负实数矩阵元素的一条运算性质与一类不等式的证明  

On a Operation Property of Non-negative Real Matrixes and the Proof of A Class of Inequalities

作　　者：蔡广平 

机构地区：[1]长沙职工大学,长沙410015

出　　处：《数学理论与应用》2003年第2期56-60,共5页Mathematical Theory and Applications

摘　　要：n× m非负实数矩阵的每列元素之和的几何平均值不小于其每行元素的几何平均值之和 ,运用它给出了一类和 (或积 )式不等式的简捷证明 ,也导出了著名不等式 :Cauchy不等式。In this paper,by appliying the property that the geometric average of the sum of elements of the column of a n×m real matrix is non-lower than the sum of the geometric average of elements of the row,the simple and direct proof of the class of inequalities on sum or product is agined,for celebrated Cauchy-inequality and Holder-inequality,their extend form are derived.

关 键 词：实矩阵 矩阵元素 CARLSON不等式 算术-几何平均值不等式 幂平均不等式 CAUCHY不等式 MINKOWSKI不等式 Holder不等式 

分 类 号：O151.21[理学—数学] O151.25[理学—基础数学]