∀ {m : Type u_1} {n : Type u_2} {R : Type u_4} [inst : Fintype m] [inst_1 : Fintype n] [inst_2 : PartialOrder R]
  [inst_3 : NonUnitalRing R] [inst_4 : StarRing R] [StarOrderedRing R] [NoZeroDivisors R] (A : Matrix m n R)
  (v : n → R), ((A.conjTranspose * A).mulVec v = 0) = (A.mulVec v = 0)