Category:Definitions/Central Dilatation Mappings

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

Definition 1

Let $K$ be a field.

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

Let $\lambda \in K$.

The central dilatation 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 $x$.

Definition 2

A central dilatation mapping is a linear transformation involving a fixed point $C$ such that the image $P'$ of a point $P$ is the point on the directed line segment $CP$ such that $CP' = k CP$ where $k$ is a real non-zero constant.