Category:Definitions/Similarity Mappings

This category contains definitions related to Similarity Mappings.
Related results can be found in Category:Similarity Mappings.

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).