A note on the canonical form for a pair of orthoprojectors

Let $P$ and $Q$ be orthoprojectors in $\mathbb C^n$. The canonical form for $P$ and $Q$ is constracted as their common block diagonal form with diagonal blocks of order one or two. The entries in the $2\times 2$ blocks of the canonical form are then interpreted in terms of the canonical angles between the subspaces $\mathcal L=\operatorname{im}P$ and $\mathcal M=\operatorname{im}Q$.