To find out the new decomposition, the new λ λ 's at the bond k and their corresponding Schmidt eigenvectors must be computed and expressed in terms of the Γ Γ 's of the decomposition D. The reduced density matrix ρ ρ ′ [ D K ] is therefore diagonalized : ρ ρ ′ [ D K ] = T r J C | ψ ψ ′ ⟩ ⟩ ⟨ ⟨ ψ ψ ′ | = ∑ ∑ j , j ′ , γ γ , γ γ ′ ρ ρ γ γ γ γ ′ j j ′ | j γ γ ⟩ ⟩ ⟨ ⟨ j ′ γ γ ′ | .