= Kernel of a character
{title2=$\ker\chi=\{g:\chi(g)=\chi(1)\}$}
= Character kernel
{synonym}
For a complex character $\chi$ of a <finite group>, its kernel is the kernel of an affording <group representation>. Averaging an inner product makes that representation unitary. If its degree is $d$, all eigenvalues of a group element have modulus one, so their sum equals $d$ only when every eigenvalue is one. Thus the displayed character-value criterion agrees with the representation kernel and defines a <normal subgroup>.
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