矩阵受控关系引入及其不等式  

The Introduction of the of Matrix and the Corresponding Inequalities

作　　者：靳志勇[1] 李亦芳[2] 

机构地区：[1]中国计量学院现代科技学院,浙江杭州310012 [2]华北水利水电学院数学与信息科学学院,河南郑州450011

出　　处：《河南工程学院学报（自然科学版）》2009年第3期76-80,共5页Journal of Henan University of Engineering：Natural Science Edition

基　　金：河南省自然科学基金资助项目(0611052600)

摘　　要：利用向量的受控关系,将矩阵作向量化运算,从而定义矩阵的受控关系,将向量受控的结论推广到矩阵受控,得到其他相应的结论;利用Schur函数及矩阵受控得到了推广结论;利用双随机阵,元素均相等的矩阵及单位矩阵之间的受控关系,得到了一些新的结论;推广了平均值之间的不等式关系及相应结论.In this paper, the matrix is by the use of the relation between vectors. By this means the relation between matrices is defined, and the relation between vectors is extended to the relation between matrices and some corresponding conclusions are drawn. Next by the introduction of the Schur function to the matrix several conclusions are made. By the use of doubly stochastic matrices and the relation between the matrix with equal elements and the unit matrix, some new generalization are done. Lastly the inequality relation between the averages is extended and some new conclusions are reached.

关 键 词：向量受控 矩阵向量化运算 矩阵受控 Schur函数 

分 类 号：O178[理学—数学]