\begin{definition}[Definition:Quadratic Space]
Let $\mathbb K$ be a field.
A '''quadratic space''' over $\mathbb K$ is a pair $\left({V, q}\right)$ where:
:$V$ is a vector space over $\mathbb K$ of finite dimension $n>0$
:$q$ is a quadratic form on $V$.
\end{definition}