There is more than one convenient way to describe the structure of affine groups. There is the abstract result that it is a semidirect product: this is given on the affine space page. There is a a more down-to-earth matrix representation: represent a pair (*M*, *v*) where *M* is an *n*×*n* matrix over *K*, and *v* a 1×*n* column vector, by the (*n*+1)×(*n*+1) matrix (*M**|*v**) where *M** is the *n*×(*n*+1) matrix formed by adding a row of zeroes below *M*, and *v** is the column matrix of size *n*+1 formed by adding a 1 below *v*.

*This is a stub article. Work on it.*