Definition:Affine Transformation/Definition 1

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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 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 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