Group representation is a concept from the field of abstract algebra and representation theory, which studies how groups can be represented by matrices and how their elements can act on vector spaces. Essentially, a group representation provides a way to express abstract group elements as linear transformations (or matrices) acting on a vector space. ### Key Concepts: 1. **Group**: A set equipped with an operation that satisfies four properties: closure, associativity, the existence of an identity element, and the existence of inverses.
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A group representation is a group homomorphism from a group to the general linear group of a vector space. It realizes abstract group elements as invertible linear transformations.