In this formulation, the state of a physical system corresponds to a vector of length 1 in a Hilbert space H over the complex numbers. An observable is represented by a self-adjoint (i.e. Hermitian) operator A on H. If H is finite dimensional, by the spectral theorem, A has an orthonormal basis of eigenvectors. If the system is in state ψ, then immediately after measurement the system will occupy a state that is an eigenvector e of A and the observed value λ will be the corresponding eigenvalue of the equation Ae = λe. It is immediate from this that measurement in general will be non-deterministic. Quantum mechanics, moreover, gives a recipe for computing a probability distribution Pr on the possible outcomes given the initial system state is ψ. The probability is Pr ⁡ ⁡ ( λ λ ) = ⟨ ⟨ E ⁡ ⁡ ( λ λ ) ψ ψ ∣ ∣ ψ ψ ⟩ ⟩ where E (λ) is the projection onto the space of eigenvectors of A with eigenvalue λ.