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 if and only if:

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

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

Also known as

An affine transformation is also known as an affine mapping.

Some sources refer to it as an affinity.

Also see

• Equivalence of Definitions of Affine Transformation

• Results about affine transformations can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): affine transformation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): affine transformation