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