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
Article
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.
Connections
complex number
Entity
bijection
Entity
irreducible representation
Entity
mathematics
Entity
physics
Entity
International Standard Book Number
Entity
prime number
Entity
function
Entity
linear algebra
Entity
real number
Entity
set
Entity
digital object identifier
Entity
group
Entity
vector space
Entity
group theory
Entity
crystallography
Entity
OCLC, Inc.
Entity
composite number
Entity
Fourier transform
Entity
continuous function
Entity