摘要
主要研究了矩阵方程组AX=B,XC=E的中心对称解与反中心对称解。利用中心对称(反中心对称)矩阵的性质,给出了矩阵方程组中心对称解(反中心对称解)存在的充分必要条件和解的一般表达式。进而讨论了对任意给定矩阵的最佳逼近问题,并给出了问题1的最佳逼近解。
In this article,the centrosymmetric solution and the anti-centrosymmetric solution of matrix equations AX=B,XC=E is considered.With special properties of centrosymmetric(anti-centrosymmetric)matrices, the necessary and sufficient conditions for the solvability and the general expression of the centrosymmetric solution(anti-centrosymmetric solution)are obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set is solved.
出处
《东北电力大学学报》
2010年第2期68-73,共6页
Journal of Northeast Electric Power University
关键词
矩阵方程
中心对称矩阵
反中心对称矩阵
最佳逼近
matrix equations
centrosymmetric matrix
anti-centrosymmetric matrix
optimal approximation
