The solution of the matrix equation [formula omitted] and the system of matrix equations [formula omitted] with [formula omitted

Abstract

In this paper, the solvability conditions for the matrix equation AXB=D and a pair of matrix equations AX=C,XB=D with the constraint X*X=Ip are deduced by applying the spectral and singular value decompositions of matrices, and the expressions of the general solutions to these matrix equations are also provided. Furthermore, the associated optimal approximate problems to the given matrices are discussed and the optimal approximate solutions are derived. Finally, two numerical experiments are given to validate the accuracy of the results.