(* The annihilator of a single vector. *)
Definition annihilator_mx u := (E_G :&: kermx (lin_mul_row u))%MS.

(* Specifications: *)
Lemma annihilator_mxP u A :
reflect (A \in E_G /\ u *m A = 0)%MS (A \in annihilator_mx u)%MS.