\begin{definition}[Definition:Similarity Mapping/Scale Factor]
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 $G$:
:$\forall \mathbf x \in G: \map {s_\beta} {\mathbf x} = \beta \mathbf x$
The coefficient $\beta$ is called the '''scale factor''' of $s_\beta$.
\end{definition}