Let (mathbf{P}) be a projection matrix. Show that the diagonal elements of (mathbf{P}) all lie in the

Question:

Let $\mathbf{P}$ be a projection matrix. Show that the diagonal elements of $\mathbf{P}$ all lie in the interval $[0,1]$. In particular, for $\mathbf{P}=\mathbf{X X}^{+}$in Theorem 5.1, the leverage value $p_{i}:=\mathbf{P}_{i i}$ satisfies $0 \leqslant p_{i}$ $\leqslant 1$ for all $i$.

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