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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“This is the frost coming out of the ground; this is Spring. It precedes the green and flowery spring, as mythology precedes regular poetry. I know of nothing more purgative of winter fumes and indigestions. It convinces me that Earth is still in her swaddling-clothes, and stretches forth baby fingers on every side.”
—Henry David Thoreau (1817–1862)