 Representation theory of groups

Representation theory of groups is a branch of mathematics that studies how groups can be represented through linear transformations of vector spaces. More formally, a representation of a group \( G \) is a homomorphism from \( G \) to the general linear group \( GL(V) \) of a vector space \( V \). This means that each element of the group is associated with a linear transformation, preserving the group structure.