一类性质没有Hermitian矩阵优但比一般矩阵良的矩阵  

A set of matrix whose properties are not as good as Hermitian matrix but better than generic ones

作　　者：田咏梅 刘慧娟 王超 TIAN Yongmei;LIU Huijuan;WANG Chao(General Education Center,Zhengzhou Business University,Gongyi 451200,China)

机构地区：[1]郑州商学院通识教育中心,河南巩义451200

出　　处：《南阳师范学院学报》2022年第6期18-21,共4页Journal of Nanyang Normal University

基　　金：国家自然科学基金资助项目(11961076)。

摘　　要：受Hermitian矩阵启发,发现了一类新的矩阵,即适于条件A∈C n×n,A=A 4的矩阵.应用正规矩阵、矩阵的奇异值、特征值概念、德·费弗公式证明了适于这种条件的矩阵是正规矩阵,获得了这类矩阵的谱,奇异值分解式和逆矩阵表示式.举例并进行了这种矩阵在性质方面与Hermitian矩阵和一般矩阵的比较.Inspired by Hermitian matrix,the matrix that suits to A∈C n×n,A=A 4 is discovered.Utilizing both the concepts of normal matrix,the singular value and eigenvalue of matrix,and De Fever formula,the matrix A mentioned above is found and proved to be normal matrix.The singular value decomposition,the invasion matrix expression of such matrix are also investigated.Some examples are used to explain that this matrix has some properties not to be as good as Hermitian matrix but better than the generic ones.These conclusions will enrich the theory of normal matrix.

关 键 词：正规矩阵 矩阵的谱 奇异值分解 

分 类 号：O151.21[理学—数学]