The square roots of its eigenvalues are the new λ λ 's. Expressing the eigenvectors of the diagonalized matrix in the basis: { | j γ γ ⟩ ⟩ } the Γ Γ [ D ] 's are obtained as well: | Φ Φ ′ [ D K ] ⟩ ⟩ = ∑ ∑ j , γ γ Γ Γ β β γ γ ′ [ D ] j λ λ γ γ | j γ γ ⟩ ⟩ .