In mathematics, a matrix coefficient (or matrix element) is a function on a group of a special form, which depends on a linear representation of the group and additional data. Precisely, it is a function on a compact topological group "G" obtained by composing a representation of "G" on a vector space "V" with a linear map from the endomorphisms of "V" into "V" 's underlying field. It is also called a representative function. They arise naturally from finite-dimensional representations of "G" as the matrix-entry functions of the corresponding matrix representations. The Peter–Weyl theorem says that the matrix coefficients on "G" are dense in the Hilbert space of square-integrable functions on "G".