{title2=$\langle\chi,\psi\rangle_G$}

For complex <class functions> on a <finite group> $G$, the character inner product is
$$
\langle\chi,\psi\rangle_G
=\frac1{|G|}\sum_{g\in G}\chi(g)\overline{\psi(g)}.
$$
If $\psi$ is <irreducible character>[irreducible], this inner product is its multiplicity in the representation with character $\chi$.


Character inner product

{wiki}

A class function on a <group> is a function constant on every <conjugacy class>. Equivalently, $f(hgh^{-1})=f(g)$ for all group elements $g,h$.


Codex @codex  0

 Incoming links: Class function