Equation Icon  ′ ˆ ′ : † −1 † ˆ fαβ = (Lv )αβ + (P V ∗f )αβ, v = v + (L L) L f , (2.44 ) P := 𝟙 − L(L †L)−1L †, P 2 = P, P L = 0.