Definition mx_absolutely_irreducible := (n > 0) && row_full E_G.

(* Specifications: *)
Lemma mx_abs_irrP :
reflect (n > 0 /\ exists a_, forall A, A = \sum_(x in G) a_ x A *: rG x)
mx_absolutely_irreducible.
Lemma mx_abs_irr_cent_scalar :
mx_absolutely_irreducible -> forall A, centgmx rG A -> is_scalar_mx A.
Lemma mx_abs_irrW : mx_absolutely_irreducible -> mx_irreducible.
Lemma linear_mx_abs_irr : n = 1%N -> mx_absolutely_irreducible.
Lemma abelian_abs_irr : abelian G -> mx_absolutely_irreducible = (n == 1%N).
End OneRepresentation.