矩阵方程AX=B,XC=D的定秩解
THE EXTREMAL RANK SOLUTIONS OF THE MATRIX EQUATIONS AX = B, XC = D

本文研究了一类矩阵方程组解的秩的范围.利用矩阵的奇异值分解以及Frobenius范数的特征,得到了解的极值秩以及解的通式,并就这些问题的特殊情况进行了讨论,得到了一些结果.
In this paper, we considered the rank range of the solutions of a class of matrix equations. By applying the singular value decomposition of matrix and the properties of Frobenius matrix norm, we obtained the extremal rank and the solution expression of under rank constrained. Some special cases of theses problems are considered, and some results are obtained