一类新的可对角化矩阵及其张量积与张量和

A new kind of diagonalizable matrix with its tensor product and tensor sum

应用正规矩阵、共轭转置矩阵的概念和理论,研究了适于条件A=A 2-I的矩阵A的特征值分布。利用矩阵张量积与张量和理论,获得了适于上述条件的两个矩阵A,B的张量积与张量和的表达式及其行列式的值,给出了适于这一条件的矩阵的张量积、张量和仍属于此类型的矩阵的充要条件。

By applying the concepts and theories of normal matrices and conjugate transpose matrices,the eigenvalue distribution of matrix A*=A 2-I suitable for conditions has been studied.By using the theory of matrix tensor product and tensor sum,the expressions and determinant values of tensor product and tensor sum for two matrices A and B that are suitable for the above conditions are obtained.The necessary and sufficient conditions for tensor product,tensor sum,and matrices that still belong to this type of matrix which are suitable for this condition are given.