character

Let $ρ$ be a group representation. Then, the character $χ_{ρ} (g)$ of a group element $g$ is the trace of the matrix representation of $g$ : $T r (ρ (g))$

The character is invariant under similarity transforms (see matrix similarity) because $T r (U A U^{- 1}) = T r (U^{- 1} U A) = T r (A)$