When an observable A has a pure point spectrum, it can be written in terms of an orthonormal basis of eigenvectors. That is, A has a spectral decomposition A = ∑ ∑ λ λ λ λ E A ⁡ ⁡ ( λ λ ) where E A (λ) is a family of pairwise orthogonal projections, each onto the respective eigenspace of A associated with the measurement value λ.