关于矩阵方程组AX=C,XB=D的最小二乘解和极小范数最小二乘解

Least squares solution and minimum-norm least-squares solution of matrix equations AX=C,XB=D

借助Kronecker积将一般的矩阵方程组AX=C,XB=D进行巧妙变形,再利用矩阵的方块技巧和广义逆矩阵方法,给出了它们的最小二乘解以及极小范数最小二乘解.

In this paper,by means of Kronecker product,the general matrix equation AX=C,XB=D is cleverly deformed to vector form.Then using the matrix block technique and the generalized inverse matrix method,the least squares solutions and the minimal norm least squares solution are given.