矩阵方程X^TAX=B反对称解及其最佳逼近

The Anti symmetric Solution of X TAX=B and its Best Approximation

讨论一类约束矩阵方程的反对称解及其最佳逼近问题，得到比较满意的结果。

This paper is concerned with solving the following two problems: Problem Ⅰ.Given X∈R n×m ,B∈R m×m ,find A∈ASR n×n so that ‖ X TAX-B ‖=min,where ‖·‖is Frobenius norm. ASR n×n ={A∈R n×m |A=-A T} . ProblemⅡ.Given A ∈R n×n ,find A LS ∈S E so that ‖A -A LS ‖ = min A∈SE ‖A -A‖ ,where S E denotes the solution set of problem. The general form of S E has been given.From problem Ⅱ the expression of the solution has been provided.