information:extraction, quality:corruption
Representation

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 an invertible matrix A {\displaystyle A} and the translation as the addition of a vector b {\displaystyle \mathbf {b} }, an affine map f {\displaystyle f} acting on a vector x {\displaystyle \mathbf {x} } can be represented as