Subordinate Quadratic Forms and Their Complementary Forms

Abstract

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 (z ₁,..., z _μ) = (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 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]