Image for representation functor

representation functor

A representation functor is a mathematical tool that translates abstract algebraic objects—like groups or algebras—into concrete structures such as matrices acting on vector spaces. It "represents" these abstract entities in a form that's easier to analyze, using familiar linear algebra concepts. Think of it as a way to study complex symmetries or transformations by expressing them as explicit matrix operations, making their properties more tangible and manageable within linear algebra frameworks.