In the case $n=1$: Let $X_{1} \in \mathcal{M}_{2,1}(\mathbb{R})$ have norm 1. Show that the square matrix consisting of columns $X_{1}$ and $-J_{1} X_{1}$ is both orthogonal and symplectic.
In the case $n=1$: Let $X_{1} \in \mathcal{M}_{2,1}(\mathbb{R})$ have norm 1. Show that the square matrix consisting of columns $X_{1}$ and $-J_{1} X_{1}$ is both orthogonal and symplectic.