Section LinMulRow.
Variables m n : nat.
Definition lin_mul_row u : 'M[R]_(m * n, n) := lin1_mx (mulmx u \o vec_mx).
Canonical lin_mul_row_additive := Additive lin_mul_row_is_linear.
Canonical lin_mul_row_linear := Linear lin_mul_row_is_linear.

Lemma mul_vec_lin_row A u : mxvec A *m lin_mul_row u = u *m A.