Subordinate quadratic forms and their complementary forms

Theorem 1. For α, β on the range 1,..., μ, let Q(z) = ^*aαβzαzβ be a real valued, nonsingular, symmetric quadratic form. For positive integers r and s such that μ = r + s set (z₁,..., z_μ) = (u₁,..., u_r:S₁,..., 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 ε π_r. For an arbitrary r-tuple ω₁,..., ω_r set [Formula: see text] index H_B(ω) = κ and nullity H_B(ω) = ν. Then [Formula: see text]