(* The subspace of homomorphic images of a row vector.                        *)
Definition row_hom_mx u :=
(\bigcap_j kermx (vec_mx (row j (annihilator_mx u))))%MS.

Lemma row_hom_mxP u v :
reflect (exists2 f, u <= dom_hom_mx f & u *m f = v)%MS (v <= row_hom_mx u)%MS.