Introduction to Representation Theory
《Introduction to Representation Theory》 · 第 68–69 页 · Section 4.6「Unitary representations. Another proof of Maschke's theorem for complex representations」，Definition 4.6.1
Definition 4.6.1. A unitary finite dimensional representation of a group $G$ is a representation of $G$ on a complex finite dimensional vector space $V$ over $\mathbb C$ equipped with a $G$-invariant positive definite Hermitian form $(\,,\,)$, i.e., such that $\rho_V(g)$ are unitary operators: $(\rho_V(g)v,\rho_V(g)w)=(v,w)$.