group representation
Sign in to saveAlso known as representation of a group, representations of a group, representations of groups
group homomorphism into the general linear group over a vector space
~14 min read
Encyclopedic overview
A representation of a group "acts" on an object. A simple example is how the symmetries of a regular polygon, consisting of reflections and rotations, transform the polygon.
In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication.
Excerpted from Wikipedia’s “group representation” article, available under the CC BY-SA 4.0 licence.