= Reduced matrix element
{title2=$A(e_i\otimes v_s)=\sum_\nu g_\nu C^\nu_{ris}v_r$}
A tensor operator transforming in an <irreducible representation> $R$ between states in $V$ defines an <intertwining operator> $R\otimes V\to V$. In a basis of these intertwining maps, its scalar coefficients $g_\nu$ are reduced matrix elements, independent of the component indices. <Schur lemma> makes the number of independent coefficients the multiplicity of $V$ in $R\otimes V$. The component dependence is fixed by the associated <Clebsch-Gordan coefficients>.
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