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.
Categories: math.RA