求解矩阵方程AXB^T+CYD^T=T的一般解

General solutions of matrix equation AXB^T+CYD^T=T

对于矩阵方程AXBT+CYDT=T,将其作为在列分块E=[A,C]和F=[B,D]下EZFT=T的块对角约束问题,其中Z=diag(X,Y).通过QR和CS分解,从无约束矩阵方程EZFT=T的通解中得到相应块对角解的简洁表达式.

The matrix equation AXB^T ＋CYD^T= T is considered as the block diagonal constrained problem of EZF^T = T with the column blocks E= [A,C] and F= [B, D], where Z= diag（X,Y）. By means of QR and CS decompositions, simple representations of block diagonal solutions to matrix equation EZF^T= T are obtained from the general solutions to its unconstrained problem.