Canonical horner_mx_lrmorphism := [lrmorphism of horner_mx].
Definition powers_mx d := \matrix_(i < d) mxvec (A ^+ i).

(* Specifications: *)
Lemma horner_rVpoly m (u : 'rV_m) :
horner_mx (rVpoly u) = vec_mx (u *m powers_mx m).