transform

In mathematics, particularly in semigroup theory, a transformation is any function f mapping a set X to itself, i.e. f:X’X. In other areas of mathematics, a transformation may simply be any function, regardless of domain and codomain. This wider sense shall not be considered in this article; refer instead to the article on function for that sense. Examples include linear transformations and affine transformations, 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 described explicitly using matrices.