= Clebsch-Gordan decomposition of group representations
{c}
{title2=$V\otimes W\cong\bigoplus_\lambda m_\lambda V_\lambda$}
A Clebsch-Gordan decomposition expresses a <tensor product of group representations> as a <direct sum> of <irreducible representations>, whenever <complete reducibility of compact-group representations> or <Maschke's theorem> applies. For a <finite group> over the <complex numbers>, the multiplicity of $V_\lambda$ is the <character inner product> $m_\lambda=\langle\chi_\lambda,\chi_V\chi_W\rangle$. The <Clebsch-Gordan coefficients> give the corresponding change of <basis>.
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