THE LEAST-SQUARES SOLUTIONS WITH THE HERMITIAN-REFLEXIVE MATRIX FOR A CLASS OF MATRIX EQUATIONS
一类矩阵方程的埃尔米特自反最小二乘解

By means of the properties of the Hermitian-reflexive matrix and the straightened matrix, this paper considers the least-squares solutions with Hermitian-reflexive for the matrix equation $AX+BY=C.$ The necessary and sufficient condition of the solutions for the matrix equation in the sets of Hermitian-reflexive matrices and the general expression of the solution are presented. Furthermore, for any two given complex matrices, the expression of the solution for relevant optimal approximate problem is derived.