\begin{definition}[Definition:Contraction]
Let $G$ be a vector space over a field $K$.
Let $\beta \in K$.
Let $s_\beta: G \to G$ be a similarity mapping on $G$:
:$\forall \mathbf x \in G: \map {s_\beta} {\mathbf x} = \beta \mathbf x$
Let the scale factor $\beta$ be such that $0 < \beta \le 1$.
Then $s_\beta$ is called a '''contraction'''.
\end{definition}