Definition:Dilation Mapping

Definition

Let $K$ be a field.

Let $X$ be a vector space over $K$.

Let $\lambda \in K$.

We define the dilation mapping $c_\lambda : X \to X$ by:

$\map {c_\lambda} x = \lambda x$

for each $x \in X$.

Also known as

The map $c_\lambda$ may also be called the multiplication operator.

Sources

• 1991: Walter Rudin: Functional Analysis (2nd ed.) ... (previous) ... (next): $1.6$: Topological vector spaces