Subordinate Quadratic Forms and Their Complementary Forms

Theorem 1. For α, β on the range 1,..., μ, letQ (z ) =* a αβz αz β be a real valued, nonsingular, symmetric quadratic form. For positive integersr ands 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] LetB = (z (1) ,...,z (r )) be a base “overR ” for pointsz ε πr . For an arbitraryr -tuple ω1 ,..., ωr set [Formula: see text] indexHB (ω) = κ and nullityHB (ω) = ν. Then [Formula: see text]