线性流形上矩阵方程的对称次反对称最小二乘解  

The Symmetric and Sub-Anti-Symmetric Solutions of the Linear Matrix Equation on some Linear Manifolds

作　　者：钱爱林[1] 艾国荣 

机构地区：[1]咸宁学院数学与统计学院,湖北咸宁437000 [2]咸宁市温泉中学,湖北咸宁437000

出　　处：《咸宁学院学报》2009年第3期1-4,共4页Journal of Xianning University

摘　　要：设矩阵A=(aij)∈Rn×n,如果满足aij=aji=-an-j+1,n-i-1(i,j=1,2,…,n),则称A为对称次反对称矩阵,所有n阶对称次反对称矩阵的全体记为SASRn×n.本文通过矩阵的广义奇异值分解,得到了线性流形上矩阵方程ATXA=B存在对称次反对称解的充分必要条件,并且给出了解的表达式及其最佳逼近的条件.By applying the generalized singular value decomposition of matrices, this paper provides the necessary and sufficient conditions for the existence and the expression of the symmetric and sub - anti - symmet- ric solutions of the linear matrix equation on some linear manifolds. In addition, the expression of the optimal approximation solution to the given matrix is derived.

关 键 词：矩阵方程 对称次反对称矩阵 奇异值分解 最佳逼近 

分 类 号：O241.6[理学—计算数学]