For example, suppose the state space is the n -dimensional complex Hilbert space C and A is a Hermitian matrix with eigenvalues λ i, with corresponding eigenvectors ψ i. The projection-valued measure associated with A, E A, is then E A ⁡ ⁡ ( B ) = | ψ ψ i ⟩ ⟩ ⟨ ⟨ ψ ψ i | , where B is a Borel set containing only the single eigenvalue λ i. If the system is prepared in state | ψ ψ ⟩ ⟩ Then the probability of a measurement returning the value λ i can be calculated by integrating the spectral measure ⟨ ⟨ ψ ψ ∣ ∣ E A ⁡ ⁡ ψ ψ ⟩ ⟩ over B i. This gives trivially ⟨ ⟨ ψ ψ | ψ ψ i ⟩ ⟩ ⟨ ⟨ ψ ψ i ∣ ∣ ψ ψ ⟩ ⟩ = | ⟨ ⟨ ψ ψ ∣ ∣ ψ ψ i ⟩ ⟩ | 2 .