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In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication. (Def: http://en.m.wikipedia.org/wiki/Linear_map)

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, a linear function) is a mapping $V \to W$ between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication. Reference: Wikipedia.

Linear maps can generally be represented as matrices, and simple examples include rotation and reflection linear transformations.