Definition:Associated Quadratic Form

Definition
Let $\mathbb K$ be a field.

Let $V$ be a vector space over $\mathbb K$.

Let $b : V\times V \to \mathbb K$ be a bilinear form.

The quadratic form associated to $b$ is the quadratic form:
 * $q : V \to \mathbb K : x \mapsto b(x, x)$

Also see

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