# Equivalent orthogonal representations are orthogonaly equivalent

Could anyone point me to a reference for the following fact :

Let $G$ denote the orthogonal or symplectic complex group and $H$ be a complex Lie group, then if $\rho_1\,:H\, \rightarrow G$, $\rho_2\,:H\, \rightarrow G$ are two equivalent representations (conjugated by the linear group), they are conjugated by the group $G$.