Subordinate quadratic forms and their complementary forms.
Theorem 1. For alpha, beta on the range 1,..., mu, let Q(z) = (*)aalphabetazalphazbeta be a real valued, nonsingular, symmetric quadratic form. For positive integers r and s such that mu = r + s set (z(1),..., z(mu)) = (u(1),..., u(r):S(1),..., S(n)), Q(z) = P(u, s) and [Formula: see text] Let B = (z((1)),..., z((r))) be a base "over R" for points z epsilon pi(r). For an arbitrary r-tuple omega(1),..., omega(r) set [Formula: see text] index H(B)(omega) = kappa and nullity H(B)(omega) = nu. Then [Formula: see text].
Morse
M
M
Institute for Advanced Study, Princeton, New Jersey 08540.