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 ${\rm {\bf A}}{\rm {\bf X}} = {\rm {\bf B}}$, ${\rm {\bf X}}{\rm {\bf A}} = {\rm {\bf B}}$ and ${\rm {\bf A}}{\rm {\bf X}}{\rm {\bf B}} ={\rm {\bf 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.