An expression of the general common least-squares solution to a pair of matrix equations with applications

摘要

In this paper, an explicit representation of the general common least-squares solution to the pair of matrix equations A_1,XB_1, = C_1 and A_2XB_2 = C_2 is obtained. Furthermore, we use this result to determine the condition for the existence of a Hermitian least-squares solution to the matrix equation AXB = C, and the expression of the general Hermitian least-squares solution is also given. Special attention is paid to consider the existence of Hermitian {1, ('[-inverses of A, i = 3, 4, and the representations of the Hermitian generalized inverses are presented. Finally, a numerical example is given to illustrate our result.