Definition:Affine Transformation/Definition 2
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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
- 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