Section Diag.
Variable (F : fieldType).
Hint Resolve diagonalizable_diag : core.
Hint Resolve diagonalizable0 : core.

Lemma diagonalizablePeigen {n} {A : 'M[F]_n} :
diagonalizable A <->
exists2 rs, uniq rs & (\sum_(r <- rs) eigenspace A r :=: 1%:M)%MS.