= Character orthogonality for compact groups
{title2=$\int_G\chi_V\overline{\chi_W}\,dg=\dim\operatorname{Hom}_G(W,V)$}
For finite-dimensional <unitary representations> of a <compact group>, average the action on $\operatorname{Hom}(W,V)$ against normalized <Haar measure>. This is the <orthogonal projection> onto the <intertwining operators>, and its <trace> is the displayed integral. The <Schur lemma> therefore makes distinct <irreducible> <characters> <orthogonal> and each <irreducible> <character> of norm one.
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