In order to relate the two vectors | f ⟩ ⟩ and | g ⟩ ⟩ , we use the Cauchy–Schwarz inequality which is defined as ⟨ ⟨ f ∣ ∣ f ⟩ ⟩ ⟨ ⟨ g ∣ ∣ g ⟩ ⟩ ≥ ≥ | ⟨ ⟨ f ∣ ∣ g ⟩ ⟩ | 2 , and thus Equation (1) can be written as