End LinRowVector.
(* Correspondance between matrices and linear function on matrices. *)
Section LinMatrix.
Variables m1 n1 m2 n2 : nat.
Definition lin_mx (f : 'M[R]_(m1, n1) -> 'M[R]_(m2, n2)) :=
lin1_mx (mxvec \o f \o vec_mx).
Variable f : {linear 'M[R]_(m1, n1) -> 'M[R]_(m2, n2)}.

(* Specifications: *)
Lemma mul_rV_lin u : u *m lin_mx f = mxvec (f (vec_mx u)).
Canonical lin_mulmxr_additive := Additive lin_mulmxr_is_linear.