约束线性矩阵方程的求解

Solutions of a Restricted. Linear Matrix Equation

本文研究了一般的约束线性矩阵方程ＡＸＢ＝Ｄ，Ｒ（Ｘ）Ｔ，Ｎ（Ｘ）Ｓ其中Ａ∈ｍｘｎ，Ｂ∈ｐｘｑ，Ｄ∈ｍｘｑ，Ｔ和Ｓ分别为ｎ和ｐ的子空间。给出了上式有解与有唯一解的充要条件。

Considers a general restricted linear matrix equation AXB=D,R(X)  T,N(X)S. Where A∈ m×n B∈ p×q ,D∈ m×q , and T and S are subspace of  n and  p ,respectively.On this basis,the necessary and sufficient condition for this equation to have a unique solutions,moreover,the representations of general solutions and unique solution are given.