《一类可以对角化的矩阵》一文的进一步研究结果  

Further results on article of a class of matrices that can be diagonalized

作　　者：宫玉荣 刘慧娟 GONG Yurong;LIU Huijuan(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：《轻工学报》2021年第3期104-108,共5页Journal of Light Industry

基　　金：国家自然科学基金项目(11801529)。

摘　　要：利用矩阵特征值与其行列式的关系及矩阵的奇异值、张量积、张量和等概念和理论,用另一种方法证明了文献[1]的定理2,研究了适合条件A^(*)=A^(2)的矩阵A的奇异值分解式及行列式,给出了适于这一条件的两个矩阵A与B的张量积也满足条件(A■B)^(*)=(A■B)^(2)的一些基本结果,以及A^(*)与A的特征值、特征向量之间的关系、矩阵A的谱分解式等.By utilizing the concepts and theories of singular value,tensor product,tensor sum and the connection of eigenvalue with determinant of matrices,another proof on theorem 2 in literature[1]was given,the singular value and spectral decomposition and the determinant of the matrix suited to A^(*)=A^(2) were investigated,the conclusions were also obtained:(A■B)^(*)=(A■B)^(2) on tensor product about two matrices A and B which satisfied the above condition,the relationship of eigenvalues of A^(*)with A,the relationship between eigenvectors,and spectral decomposition formular of the matrice A.

关 键 词：共轭转置矩阵 矩阵对角化 奇异值分解 张量积 

分 类 号：O151.21[理学—数学]