Transformation (mathematics)

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In mathematics, a transformation in elementary terms is any of a variety of different operations from geometry, such as rotations, reflections and translations. These can be carried out in Euclidean space, particularly in dimensions 2 and 3. They are also operations that can be performed using linear algebra, and explicitly using matrix theory.

For example, in 3D computer graphics, the operations of moving, scaling, or rotating a 3D model are commonly called transformations.

More generally, a transformation in mathematics is one facet of the mathematical function; the term mapping is also used in ways that are quite close synonyms. A transformation is, most often, an invertible function from a set X to itself; but this is not always assumed. In a sense the term transformation only flags that a function's more geometric aspects are being considered (for example, with attention paid to invariants).

A strong non-linear transformation applied to a plane through the origin
Before After
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See also