Section CentHom.
Variable f : 'M[R]_n.
Definition rcent := [set x in G | f *m rG x == rG x *m f].
Canonical rcent_group := Group rcent_group_set.
Definition centgmx := G \subset rcent.
End CentHom.
(* Representation kernel, and faithful representations. *)
Definition rker := rstab 1%:M.
Canonical rker_group := Eval hnf in [group of rker].
(* Representation center. *)
Definition rcenter := [set g in G | is_scalar_mx (rG g)].
Fact rcenter_group_set : group_set rcenter.
Canonical rcenter_group := Group rcenter_group_set.

Lemma rcenter_normal : rcenter <| G.