\begin{definition}[Definition:Similarity Mapping]
Let $G$ be a vector space over a field $K$.
Let $\beta \in K$.
Let $s_\beta: G \to G$ be the mapping on $G$ defined as:
:$\forall \mathbf x \in G: \map {s_\beta} {\mathbf x} = \beta \mathbf x$
$s_\beta$ is called a '''similarity (mapping)'''.
\end{definition}