线性流形上D反对称矩阵反问题的最小二乘解

Least-squares Solutions of Inverse Problems for D-anti-symmetric Matrix on Linear Mainfold

研究了线性流形上 D反对称矩阵反问题的最小二乘解及其逼近问题 .给出了最小二乘解的一般表达式 ,并就该问题的特殊情况 :矩阵反问题 ,证明了可解的充要条件 ,并在有解的条件下给出了解的一般表达式 .得到了最佳逼近解的表达式 .

The least squares solutions of inverse problems for D anti symmetric matrices on the linear manifold was discussed,and the general expression of the solution was obtained.Moreover,the necessary and sufficient conditions of the solvability and the expression of the general solution for inverse problem of this matrices were given.For any n by n real matrix,it's optimal approximation was obtained.