Solution
= Solution
A complex <character of a representation> of a finite <group> $G$ is the function
$$
\boxed{\chi(g)=\operatorname{tr}(\rho(g)),}
$$
where $\rho:G\to\operatorname{GL}(V)$ is a finite-dimensional complex <group representation>. The <character> is a <class function> because <trace> is unchanged by conjugation. Its degree is $\chi(1)=\dim V$.