Transformation (function)

"Transformation (mathematics)" redirects here. For other uses, see Transformation (disambiguation).
For broader coverage of this topic, 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.

In mathematics, a transformation, transform, or self-map[1] is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X.[2][3][4] 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]

  1. ^ "Self-Map -- from Wolfram MathWorld". Retrieved March 4, 2024.
  2. ^ Olexandr Ganyushkin; Volodymyr Mazorchuk (2008). Classical Finite Transformation Semigroups: An Introduction. Springer Science & Business Media. p. 1. ISBN 978-1-84800-281-4.
  3. ^ Pierre A. Grillet (1995). Semigroups: An Introduction to the Structure Theory. CRC Press. p. 2. ISBN 978-0-8247-9662-4.
  4. ^ Wilkinson, Leland (2005). The Grammar of Graphics (2nd ed.). Springer. p. 29. ISBN 978-0-387-24544-7.
  5. ^ "Transformations". www.mathsisfun.com. Retrieved 2019-12-13.
  6. ^ "Types of Transformations in Math". Basic-mathematics.com. Retrieved 2019-12-13.