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

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.