character

Let \(\rho\) be a group representation. Then, the character \(\chi_\rho(g)\) of a group element \(g\) is the trace of the matrix representation of \(g\): \(Tr(\rho(g))\)

The character is invariant under similarity transforms (see matrix similarity) because \(Tr(UAU^{-1}) = Tr(U^{-1}UA) = Tr(A)\)