Transformation (function)
In mathematics, a transformation is a function f (usually with some geometrical underpinning) that maps a set X to itself, i.e. f : X → X.[1][2][3] In other areas of mathematics, a transformation may simply refer to any function, regardless of domain and codomain.[4] For this wider sense of the term, see function (mathematics).
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Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations.[5][6]
More generally, a transformation in mathematics means a mathematical function (synonyms: "map" or "mapping"). A transformation can be an invertible function from a set X to itself, or from X to another set Y. The choice of the term transformation may simply indicate that the geometric aspects of a function are being considered (for example, with respect to invariants).