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

Abstract

In this paper, an explicit representation of the general common least-squares solution to the pair of matrix equations A 1 X B 1 = C 1 and A 2 X B 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 A X B = 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 , i } -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.