Let ρ ρ be a representation i.e. a homomorphism ρ ρ : G → → G L ( V ) of a group G where V is a vector space over a field F . If we pick a basis B for V , ρ ρ can be thought of as a function (a homomorphism) from a group into a set of invertible matrices and in this context is called a matrix representation. However, it simplifies things greatly if we think of the space V without a basis.