Overview
A representation is a map from some algebraic object, typically a group, to a linear transformation on some vector space, {% V %}.
{% D:G \rightarrow GL(V) %}
where {% GL(V) %} is the group of linear transformations on {% V %}. Because linear transformations
can be represented by
matrices,
this definition effectively says that a representation is a map between an algebraic object and a matrix that
represents it in some way.