Basic Definitions
All the linear representations in this article are finite dimensional and assumed to be complex unless otherwise stated. A representation of G is a group homomorphism ρ:G → GL(n,C) from G to the general linear group GL(n,C). Thus to specify a representation, we just assign a square matrix to each element of the group, in such a way that the matrices behave in the same way as the group elements when multiplied together.
We say that ρ is a real representation of G if the matrices are real. In other words if ρ(G) ⊂ GL(n,R).
Read more about this topic: Representation Theory Of Finite Groups
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