An alternative (equivalent) definition often used is that D satisfies D = D ⊥ ⊥ , where orthogonality is with respect to the symmetric bilinear form on V × × V ∗ ∗ given by ⟨ ( u , α α ) , ( v , β β ) ⟩ = ⟨ α α , v ⟩ + ⟨ β β , u ⟩ .