矩阵方程的AXB+CYD=E反对称极小范数最小二乘解  

LEAST SQUARES ANTI-SYMMETRIC SOLUTION OF THE MATRIX EQUATION AXB+CYD=E WITH THE LEAST NORM

作　　者：李水勤[1] 邓继恩[1] 

机构地区：[1]河南理工大学数学与信息科学院,河南焦作454003

出　　处：《南阳理工学院学报》2010年第2期95-98,共4页Journal of Nanyang Institute of Technology

摘　　要：对任意给定的矩阵A∈Rm×n,B∈Rn×s,C∈Rm×k,D∈Rk×s,E∈Rm×s,本文利用矩阵的拉直算子,Moore-Pen-rose(M-P)广义逆及Kronecker积,研究矩阵方程AXB+CYD=E的反对称最小二乘解,给出了解的表达式。并由此给出了该方程的反对称极小范数最小二乘解的表达式,同时给出了该方程有反对称解的充分必要条件及反对称解的表达式。Given matrices A∈R^m×n,B∈n×s,C∈R^m×k,D∈R^k×s,E∈R^m×s, the least-squares anti-symmetric solution of the matrix equation AXB ＋ CYD = E is studied by using Moore-Penrose generalized inverse and Kronecker product, and its expression is given in this article. Based on this, the expression of the least-squares anti-symmetric solution is deprived with the least norm, the necessary and sufficient conditions for the existence of the anti-symmetric solution and its expression are also presented.

关 键 词：反对称矩阵 极小范数解 最小二乘解 Moore—Penrose广义逆 KRONECKER积 

分 类 号：O151.21[理学—数学]