Quadratic Forms Sample Clauses

Quadratic Forms. ‌ In this section we introduce the basic theory of quadratic forms, we outline their classification, and we prove some combinatorial results that will be useful later on in this work. Our main reference is [44]. More specific references will be given throughout the section. Let K be a finite field and let V be a finite-dimensional K-vector space.
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Quadratic Forms. ‌ In this section we state the results that we need in the proof of our Main Theorem, as well as the definitions necessary to read such results. For a more involved discussion, see Section 2.4, where we include full proofs of the results stated here as well. Even though these can be found, at least partly, in the literature, we have felt it necessary to derive what we need in a unified way. Throughout this section, let K be an arbitrary field and let V be a finite dimensional K-vector space. Definition 3.3.1. A quadratic form on V is a map Q : V → K such that
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