∀ {n : Type u_2} {R : Type u_3} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [inst_3 : Fintype n]
  [Nontrivial R] [IsOrderedCancelAddMonoid R] [Nonempty n] {A : Matrix n n R}, A.PosDef → 0 < A.trace