Page "Affine transformation" Paragraph 20

As shown above, an affine map is the composition of two functions: a translation and a linear map.

Ordinary vector algebra uses matrix multiplication to represent linear maps, and vector addition to represent translations.

Formally, in the finite-dimensional case, if the linear map is represented as a multiplication by a matrix A and the translation as the addition of a vector, an affine map acting on a vector can be represented as