n. a homomorphism, R, from a (usually finite) group, G, into GL(n; K), the general linear group of degree n over the field, K, where the integer n ≥ 1 is also called the degree of R. Two representations, R and S, are said to be equivalent if they have the same degree and there is a fixed c in GL(n; K) such that R(x) = c^-1S(x)c for all x in G. A representation over the complex numbers is an ordinary representation, and one over a field of prime characteristic is a modular representation. An isomorphic copy within a particular class of groups such as permutation or matrix groups is a faithful representation.