Multiplicity of an irreducible representation
= Multiplicity of an irreducible representation
{title2=$m_\lambda$}
= Representation multiplicity
{synonym}
In a completely reducible <group representation> $V=\bigoplus_\lambda m_\lambda V_\lambda$, the nonnegative integer $m_\lambda$ counts the copies of the corresponding <irreducible representation>. For complex <representations> of a finite <group>, <character orthogonality> gives $m_\lambda=\langle\chi_\lambda,\chi_V\rangle$.