I need to show that $\bar h= \sum{h_{ii}/n} = \operatorname{Tr}[H]/n = (p+1)/n$
Using the fact that $\operatorname{Tr}[AB]=\operatorname{Tr}[BA]$ and $H=X(X^TX)^{-1}X^T$.
But I have no idea how to calculate $\bar h$, I'm betting the first equality works out because $H$ is a symmetric idempotent matrix. I also have no clue what $\operatorname{Tr}[H]$ means, I have never seen this notation before an cannot find it in my notes.