子矩阵约束下矩阵方程XA=B的对称非负定解

The Symmetric Nonegative Definite Solutions of Linear Matrix Equation XA=B

利用矩阵的广义逆及奇异值分解 ,给出了子矩阵约束下线性矩阵方程XA =B有对称非负定解的充分必要条件 ,并在有解时 。

Using the singular value decomposition and Moore-Penrose inverse of matrices,this paper gives the necessary and sufficient conditions for the symmetric nonegative definite solutions of linear matrix equation XA=B,and gives general form of the solutions if the equation XA=B is solvable.\;