Definition:Affine Transformation/Definition 1

Definition
Let $\EE$ and $\FF$ be affine spaces with difference spaces $E$ and $F$ respectively.

Let $\LL: \EE \to \FF$ be a mapping.

$\LL$ is an affine transformation there exists a linear transformation $L: E \to F$ such that for every pair of points $p, q \in \EE$:
 * $\map \LL q = \map \LL p + \map L {\vec {p q} }$

Also see

 * Equivalence of Definitions of Affine Transformation