一类矩阵方程的Hermitian R-对称定秩解(英文)

THE HERMITIAN R-SYMMETRIC EXTREMAL RANK SOLUTIONS OF A MATRIX EQUATION

本文研究了矩阵方程AX=B的Hermitian R-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.

The Hermitian R-symmetric maximM 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 hermitian R-symmetric to the equation is obtained . The expressions of such solutions to this equation are also given when the solvability conditions are satisfied. In addition, corresponding minimal rank solution set to the equation and the explicit expression of the nearest matrix to a given matrix in the Frobenius norm are provided.