Definition:Associated Bilinear Form

Definition

Let $\mathbb K$ be a field of characteristic $\Char {\mathbb K} \ne 2$.

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:

$b : V \times V \to \mathbb K : \tuple {v, w} \mapsto \dfrac 1 2 \paren {\map q {v + w} - \map q v - \map q w}$

Also see

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

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