# Subordinate Quadratic Forms and Their Complementary Forms

Theorem 1. For Î±, Î² on the range 1,..., Î¼, let Q(z) = * aÎ±Î²zÎ±zÎ² be a real valued, nonsingular, symmetric quadratic form. For positive integers r and s such that Î¼ = r + s set (z 1,..., z Î¼) = (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 âover Râ for points z Îµ Ïr. For an arbitrary r-tuple Ï1,..., Ïr set Formula: see text index HB(Ï) = Îº and nullity HB(Ï) = Î½. Then Formula: see text http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings of the National Academy of Sciences PNAS

## Subordinate Quadratic Forms and Their Complementary Forms

Abstract

Theorem 1. For Î±, Î² on the range 1,..., Î¼, let Q(z) = * aÎ±Î²zÎ±zÎ² be a real valued, nonsingular, symmetric quadratic form. For positive integers r and s such that Î¼ = r + s set (z 1,..., z Î¼) = (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 âover Râ for points z Îµ Ïr. For an arbitrary r-tuple Ï1,..., Ïr set Formula: see text index HB(Ï) = Îº and nullity HB(Ï) = Î½. Then Formula: see text

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