满足条件A^*=-A^3的矩阵性质研究  

Research on the properties of matrices suited to A^*=-A^3

作　　者：刘慧娟 曲双红 LIU Huijuan;QU Shuanghong(General Education Center, Zhengzhou Business University,Gongyi 451200,China;College of Mathematics and Information Science,Zhengzhou University of Light Industry, Zhengzhou 450002,China)

机构地区：[1]郑州商学院通识教育中心,河南巩义451200 [2]郑州轻工业大学数学与信息科学学院,河南郑州450002

出　　处：《轻工学报》2020年第6期105-108,共4页Journal of Light Industry

基　　金：国家自然科学基金项目(11801529)。

摘　　要：利用正规矩阵、共轭转置矩阵、矩阵的奇异值分解等概念和理论,发现了满足条件A^*=-A^3的矩阵A是可以对角化的,也获得了该矩阵的可能特征值分布、公式(A⊗B)^*=(A⊗B)^3、奇异值分解式和公式成立的充要条件.Using the concepts and theories of normal matrix,conjugate transpose matrix and singular value decomposition and so on,the matrix A suited to A^*=-A^3 was found to be diagonalizable;other results on this kind of matrices such as distribution of the possible characteristic values,formula(A⊗B)^*=(A⊗B)^3,singular value decomposition and the sufficient and necessary conditions for the establishment of the formula were also investigated.

关 键 词：正规矩阵 共轭转置矩阵 对角化 特征值分布 矩阵性质 

分 类 号：O151.21[理学—数学]