\begin{definition}[Definition:Associated Bilinear Form]
Let $\mathbb K$ be a field of characteristic $\operatorname{char} \mathbb K\neq2$.
Let $V$ be a vector space over $\mathbb K$.
Let $q : V \to \mathbb K$ be a quadratic form.
The '''bilinear form associated to $q$''' is the bilinear form:
:$b : V \times V \to \mathbb K : (v,w) \mapsto \frac12\left( q(v+w) - q(v) - q(w) \right)$
\end{definition}