Definition rowval_gen m U :=
<<\matrix_ik
mxvec (\matrix_(i < m, k < d) (row i (val_gen U) *m A ^+ k)) 0 ik>>%MS.

Lemma mxmodule_rowval_gen m (U : 'M_(m, nA)) :
mxmodule rG (rowval_gen U) = mxmodule rGA U.