反初等矩阵的一些性质及应用  

Some properties and applications about anti-elementary matrix

作　　者：郭传好[1] 刘贝贝 GUO Chuanhao;LIU Beibei(School of Economics and Management,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学经济管理学院,杭州310018

出　　处：《浙江理工大学学报（自然科学版）》2018年第3期362-366,共5页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：国家自然科学基金项目(11501350);浙江理工大学科研启动基金项目(16092098-Y)

摘　　要：在初等矩阵性质综合研究的基础上,定义了一类反初等矩阵,并研究了其相关性质及应用。首先基于Flip-矩阵的定义,给出了一类新的矩阵-反初等矩阵的定义及其表述形式;然后研究并给出其相关基本性质以及与初等矩阵的关系;最后给出反初等矩阵在计算方面的一些应用。相关研究成果对进一步研究次对称矩阵的相关理论具有潜在的重要意义。Based on comprehensive researches on the properties of elementary matrix,a kind of anti-elementary matrixes is given and the relevant properties ad applications are studied in this paper.Firstly,the definition and the expression of a new kind of matrixes anti-elementary matrix are given according to the definition of Flip matrix.Secondly,its basic properties and the relationship with elementary matrix are studied and given.Finally,some applications about anti-elementary matrix are given.The relevant research results have potential important significance for further studying the relevant theories of sub-symmetric matrix.

关 键 词：Flip-矩阵 反初等矩阵 三对角形矩阵 VANDERMONDE矩阵 

分 类 号：O151.21[理学—数学]