# Group Representation

A group representation is a mathematical group action on a vector space.

Group representation is a college-level concept that would be first encountered in an abstract algebra course covering group theory.

### Prerequisites

Group: | A mathematical group is a set of elements and a binary operation that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property. |

Group Action: | A group action is the association of each of a mathematical group's elements with a permutation of the elements of a set. |

Vector Space: | A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space. |