线性流形上反埃尔米特广义反汉密尔顿矩阵反问题的最小二乘解及其最佳逼近问题

利用反埃尔米特广义反汉密尔顿矩阵的特征性质和矩阵的分解理论,给出了线性流形上反埃尔米特广义反汉密尔顿矩阵反问题的最小二乘解的一般表达式.运用正交投影矩阵的性质和希尔伯特空间的逼近理论,对任意给定的n阶复矩阵,证明了最佳逼近解的存在性与惟一性,并得到了最佳逼近解的表达式.

Least-squares Solutions for Inverse Problem of Anti-Hermitian Generalized Anti-Hamiltonian Matrices on the Linear Manifold and Optimal Approximation Problem

Using the properties of anti-Hermitian generalized anti-Hamiltonian matrices and decomposition theory of matrix,we obtained a general expression of the least-squares solutions for inverse problem of anti-Hermitian generalized anti-Hamiltonian matrix on the linear manifold.We established some necessary and sufficient conditions for the linear matrix equation AX=B to have a solution on the linear manifold.For any n by n complex matrix,we also derived an expression of the solution for relevant optimal approximate problem.