I was reading this question [link text](https://mathoverflow.net/questions/5772/principal-bundles-representations-and-vector-bundles)
and can't seem to see why, if $\pi: P \to B$ is a principle $G$-bundle and $$\rho:G \to GL\_n(\mathbb{C})$$ is a representation of $G$, then the total space $P \times\_{\rho} \mathbb{C}^n$ is locally trivial.