Category:Quadratic Forms

This category contains results about Quadratic Forms.
Definitions specific to this category can be found in Definitions/Quadratic Forms.

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

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

A quadratic form on $V$ is a mapping $q : V \mapsto \mathbb K$ such that:

				$\ds \forall v \in V: \forall \kappa \in \mathbb K:$	$\ds \map q {\kappa v} = \kappa^2 \map q v $
				$\ds b: V \times V \to \mathbb K:$	$\ds \tuple {v, w} \mapsto \map q {v + w} - \map q v - \map q w $				is a bilinear form

A quadratic form is a form whose variables are of degree $2$.

Subcategories

This category has the following 3 subcategories, out of 3 total.

				\(\ds \forall v \in V: \forall \kappa \in \mathbb K:\)	\(\ds \map q {\kappa v} = \kappa^2 \map q v \)
				\(\ds b: V \times V \to \mathbb K:\)	\(\ds \tuple {v, w} \mapsto \map q {v + w} - \map q v - \map q w \)				is a bilinear form