Definition:Affine Transformation/Definition 2

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 :
 * $\forall v_1, v_2 \in \EE: \map \LL {s v_1 + t v_2} = s \map \LL {v_1} + t \map \LL {v_2}$

for some $s, t \in \R$ such that $s + t = 1$.

Also see

 * Equivalence of Definitions of Affine Transformation