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

Lemma diagonalizableP n' (n := n'.+1) (A : 'M[F]_n) :
diagonalizable A <->
exists2 rs, uniq rs & mxminpoly A %| \prod_(x <- rs) ('X - x%:P).