矩阵方程AXA^T+BYB^T=C的解的秩

The Ranks of Solutions for the Matrix Equation AXA^T+BYB^T=C

利用矩阵的奇异值分解及秩的相关结论,讨论了矩阵方程AXAT+BYBT=C的解的情况,得到了解X、Y的最大秩和最小秩.

By applying the singular value decomposition and the theories on ranks, the solutions to the matrix equation ,AXA^T 4- BYB^T = C are discussed, and the minimal and maximal ranks of the solutions are obtained.