一类矩阵方程的双对称定秩解及其最佳逼近（英文）  

BISYMMETRIC MINIMAL RANK SOLUTIONS AND ITS OPTIMAL APPROXIMATION TO A CLASS OF MATRIX EQUATION

作　　者：冯天祥[1] 

机构地区：[1]东莞职业技术学院基础课部,广东东莞523808

出　　处：《数学杂志》2016年第2期285-292,共8页Journal of Mathematics

基　　金：Supported by Scientific Research Fund of Dongguan Polytechnic(2012a01)

摘　　要：本文研究了矩阵方程AX=B的双对称最大秩和最小秩解问题.利用矩阵秩的方法,获得了矩阵方程AX=B有最大秩和最小秩解的充分必要条件以及解的表达式,同时对于最小秩解的解集合,得到了最佳逼近解.In this paper, the Bisymmetric maximal and minimal rank solutions to the matrix equation AX = B and their optimal approximation are considered. By applying the matrix rank method, the necessary and sufficient conditions for the existence of the maximal and minimal rank solutions with Bisymmetric to the equation. The expressions of such solutions to this equation are also given when the solvability conditions are satisfied. In addition, in corresponding the minimal rank solution set to the equation, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm has been provided.

关 键 词：矩阵方程 双对称矩阵 最大秩 最小秩 最佳逼近解 

分 类 号：O241.6[理学—计算数学]