coordinate sum 0, which implies that they are orthogonal to F. It now follows that V has K eigenvectors in F, and for each k (1 ≤ i ≤ K), (M(k) − 1 eigenvectors in Sk each of which have the same eigenvalue λk. Conditional on p, V acts on Sk as 2pk(1 − pk)I where I is the identity matrix. (The factor 2 comes from the two chromosomes sampled for each individual.) Thus, Now and so the eigenvalues corresponding to eigenvectors of Sk are:
