With $K = J_{n}$, $\varphi(X,Y) = X^{\top} J_{n} Y$, and $P$ a symplectic and orthogonal matrix with columns $X_{1}, \ldots, X_{2n}$ satisfying the properties of Q13: Show that, for all $i \in \{1,\ldots,n\}$, $X_{i}^{J_{n}} = X_{i+n}^{\perp}$.
With $K = J_{n}$, $\varphi(X,Y) = X^{\top} J_{n} Y$, and $P$ a symplectic and orthogonal matrix with columns $X_{1}, \ldots, X_{2n}$ satisfying the properties of Q13: Show that, for all $i \in \{1,\ldots,n\}$, $X_{i}^{J_{n}} = X_{i+n}^{\perp}$.