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 $s_\beta$.

Also see

• Results about similarity mappings can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): scale factor
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): scale factor