Editing Affine transformation (section)

==Examples==
===Over the real numbers===
The functions <math>f\colon \R \to \R,\; f(x) = mx + c</math> with <math>m</math> and <math>c</math> in <math>\R</math> and <math>m\ne 0</math>, are precisely the affine transformations of the [[real line]].

===In plane geometry===
[[File:Geometric affine transformation example.png|thumb|left|A simple affine transformation on the real plane]]
[[File:2D affine transformation matrix.svg|thumb|250px|Effect of applying various 2D affine transformation matrices on a unit square. Note that the reflection matrices are special cases of the scaling matrix.]]
In <math>\mathbb{R}^2</math>, the transformation shown at left is accomplished using the map given by:

:<math>\begin{bmatrix} x \\ y\end{bmatrix} \mapsto \begin{bmatrix} 0&1\\ 2&1 \end{bmatrix}\begin{bmatrix} x \\ y\end{bmatrix} + \begin{bmatrix} -100 \\ -100\end{bmatrix}</math>

Transforming the three corner points of the original triangle (in red) gives three new points which form the new triangle (in blue).  This transformation skews and translates the original triangle.

In fact, all triangles are related to one another by affine transformations. This is also true for all parallelograms, but not for all quadrilaterals.
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