矩阵方程AXB+CYD=E的Toeplitz矩阵解

摘要

The expressions of the Toeplitz matrix solution and symmetric Toeplitz matrix solution of the matrix equation AXB + CYD = E were given in this paper by using the Kronecker product of matrices, matrices straight operator and Moore-Penrose generalized inverse. And also the expressions of the least squares solution was given.%利用矩阵的Kronecker积、矩阵的拉直算子和Moore-Penrose广义逆的有关知识,给出了矩阵方程AXB+CYD=E的Toeplitz矩阵解和对称Toeplitz矩阵解的表达式,并给出了其最小二乘解的一般形式.