Definition:Similarity Mapping

Definition
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).

Also known as
An older term for a similarity mapping is similitude.

Also see

 * Similarity Mapping is Linear Operator