The parity operator is defined by its action in the | r ⟩ ⟩ representation of changing r to −r, i.e. ⟨ ⟨ r | P | ψ ψ ⟩ ⟩ = ψ ψ ( − − r ) The eigenvalues of P can be shown to be limited to ± ± 1 , which are both degenerate eigenvalues in an infinite-dimensional state space. An eigenvector of P with eigenvalue +1 is said to be even, while that with eigenvalue −1 is said to be odd.