# 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]
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.[4][5]