Definition:Associated Bilinear Form

Definition
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:
 * $b : V \times V \to \mathbb K : (v,w) \mapsto \frac12\left( q(v+w) - q(v) - q(w) \right)$

Also see

 * Associated Bilinear Form is Bilinear Form
 * Definition:Associated Quadratic Form
 * Matrix of Associated Bilinear Form