Definition:Stretching

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 $G$:

$\forall \mathbf x \in G: \map {s_\beta} {\mathbf x} = \beta \mathbf x$

Let the scale factor $\beta$ be such that $\beta \ge 1$.

Then $s_\beta$ is called a stretching.

Also see

• Definition:Contraction

• Results about similarity mappings can be found here.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 28$. Linear Transformations: Example $28.3$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): stretching