Definition:Similarity Mapping/Scale Factor

Definition
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 $s_\beta$.