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es in Euclidean spaces, each output coordinate of an affine map is a linear function (in the sense of calculus) of all input coordinates. Another way to deal with affine transformations systematically is to select a point as the origin; then, <span>any affine transformation is equivalent to a linear transformation (of position vectors) followed by a translation. Contents [hide] 1 Mathematical definition 1.1 Alternative definition 2 Representation 2.1 Augmented matrix 2.1.1 Example augmented matrix 3 Properties 3.1 Properti