Representation theory is both an application of the group concept and important for a deeper understanding of groups. It studies the group by its group actions on other spaces. A broad class of group representations are linear representations in which the group acts on a vector space, such as the three-dimensional Euclidean space ⁠ R 3 ⁠. A representation of a group G on an n - dimensional real vector space is simply a group homomorphism ρ ρ : G → → G L ( n , R ) from the group to the general linear group. This way, the group operation, which may be abstractly given, translates to the multiplication of matrices making it accessible to explicit computations.