矩阵方程AXB+CYD=E的Toeplitz矩阵解  

Toeplitz Matrix Solutions of Matrix Equation AXB+CYD=E

作　　者：孙庆娟[1] 郭文彬[1] 王柄中[1] 

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《河南科技大学学报（自然科学版）》2012年第3期93-97,115,共5页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(10771073)

摘　　要：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。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.

关 键 词：TOEPLITZ矩阵 KRONECKER积 矩阵的拉直算子 MOORE-PENROSE广义逆 

分 类 号：O151.21[理学—数学]