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 : XX.[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).

A composition of four mappings coded in SVG,
which transforms a rectangular repetitive pattern
into a rhombic pattern. The four transformations are linear.

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).

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