Section OneRepresentation.
Variable gT : finGroupType.
Variables (G : {group gT}) (n : nat) (rG : mx_representation F G n).
Arguments rG _%group_scope : extra scopes.
Local Notation E_G := (enveloping_algebra_mx rG).
Canonical rstabs_group := Group rstabs_group_set.
Definition mxmodule := G \subset rstabs.
End Stabilisers.
Arguments mxmoduleP {m U}.

Lemma mxmodule_eigenvector m (U : 'M_(m, n)) :
mxmodule U -> \rank U = 1%N ->
{u : 'rV_n & {a | (U :=: u)%MS & {in G, forall x, u *m rG x = a x *: u}}}.