where H i j ( Λ Λ ) = ⟨ ⟨ i | H ( Λ Λ ) | j ⟩ ⟩ and G i j = ⟨ ⟨ i | j ⟩ ⟩ is the Gram matrix of the theory. In this formulation, the eigenstates of the truncated Hamiltonian are | ψ ψ α α ⟩ ⟩ = v α α i | i ⟩ ⟩ .