矩阵方程AXA^T＋BYB^T=C的对称半正定解

Symmetric Semipositive Definite Solutions to Matrix Equation AXA~т+BYB~т=C

研究矩阵方程AXA^T+BXB^T=C的对称半正定解。利用广义奇异值分解给出了该矩阵方程有解的充要条件及解的通式。

The symmetric semipositive definite solutions to the matrix equation AXAт+BYBт=C is considered. Using the generalized singular value decomposition, we derive a necessary and sufficient condition of its solutions and then give a general analytic formula of our solutions.