Definition:Dilation Mapping

Definition
Let $K$ be a field.

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

Let $\lambda \in K$.

The dilation mapping $c_\lambda : X \to X$ is defined as:


 * $\forall x \in X: \map {c_\lambda} x = \lambda x$

where $\lambda x$ denotes the scalar product of $\lambda$ with $x$.

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

Also see

 * Definition:Left Regular Representation: a similar concept in the context of algebraic structures