Section Eigenspace.
Variables (n : nat) (g : 'M_n).
Definition eigenspace a := kermx (g - a%:M).
Definition eigenvalue : pred F := fun a => eigenspace a != 0.

Lemma eigenspaceP a m (W : 'M_(m, n)) :
reflect (W *m g = a *: W) (W <= eigenspace a)%MS.