In mathematics, and in particular the theory of group representations, the regular representation of a group G is the linear representation afforded by the group action of G on itself by translation.
One distinguishes the left regular representation λ given by left translation and the right regular representation ρ given by the inverse of right translation.
Read more about Regular Representation: Finite Groups, Significance of The Regular Representation of A Group, Module Theory Point of View, Structure For Finite Cyclic Groups, Topological Group Case, Normal Bases in Galois Theory, More General Algebras
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—Henry David Thoreau (1817–1862)