Subordinate Quadratic Forms and Their Complementary Forms

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 πr. For an arbitrary r-tuple ω1,..., ωr set Formula: see text index HB(ω) = κ and nullity HB(ω) = ν. Then Formula: see text