A representation of a group G gives us a way of visualizing G as a group of matrices. To be precise, a representation is a homomorphism from G into a group of invertible matrices. We set out this idea in more detail, and give some examples of representations. We also introduce the concept of equivalence of representations, and consider the kernel of a representation.
Let G be a group and let F be or . Recall from the first chapter that GL (n, F) denotes the group of invertible n × n matrices with entries in ...