The n occ × n occ diagonal matrix Λ 2 contains the eigenvalues of ∆P elec . (It is the square of a diagonal matrix Λ that will be used in Section 3.2, where we will discover that the values λ i have their own significance.) Eigenvalues of ∆P elec are strictly non-negative, which we indicate by writing them as λ 2 i , and they are normalized such that i λ 2 i = 1 [Eq. (2.13)]. In similar fashion, we introduce a matrix U v that diagonalizes ∆P hole :