Linear Map

A linear map is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. Formally, a function f from a vector space V to a vector space W is linear if it satisfies additivity, meaning the map sends the sum of two vectors to the sum of their images, and homogeneity, meaning scaling a vector by a number before or after applying the map gives the same result. Standard examples include matrices that transform vectors of one dimension into vectors of another, rotations and reflections used in computer graphics, and differentiation and integration treated as operators on spaces of functions. Because they preserve linear combinations, linear maps are central to linear algebra and underlie the solution of systems of linear equations as well as many techniques in computer graphics, science and engineering. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/