Analogs of Cramer's rule for the least squares solutions of some matrix equations

Abstract

The least squares solutions with the minimum norm of the matrix equations $\mathbf{A}\mathbf{X}=\mathbf{B}$, $\mathbf{X}\mathbf{A}=\mathbf{B}$ and $\mathbf{A}\mathbf{X}\mathbf{B}=\mathbf{D}$ are considered in this paper. We use the determinantal representations of the Moore - Penrose inverse obtained earlier by the author and get analogs of the Cramer rule for the least squares solutions of these matrix equations.