矩阵方程AXB=C的对称最小二乘解  

Least-Squares Solutions of Matrix Equation AXB=C for Symmetric Matrices

作　　者：李水勤[1] 邓继恩[1] 

机构地区：[1]河南理工大学,河南焦作454003

出　　处：《平顶山学院学报》2010年第2期64-65,共2页Journal of Pingdingshan University

摘　　要：利用矩阵对的商奇异值分解,得到矩阵方程AXB=C的对称最小二乘解的通解表达式,同时推出了该矩阵方程对称解存在的充分必要条件,并给出了通解表达式.By applying the quotient singular value decomposition of matrix pairs,the general expression for the least-squares symmetric solutions of the matrix equation is obtained.The necessary and sufficient conditions for the existence of the symmetric solutions of the equation are derived.In addition,an expression for general solution is given.

关 键 词：商奇异值分解 对称矩阵 最小二乘解 

分 类 号：O151.21[理学—数学]