In the case $n=1$: Determine the matrices of size $2 \times 2$ that are both antisymmetric and symplectic and show that they are not diagonalizable in $\mathbb{R}$.
In the case $n=1$: Determine the matrices of size $2 \times 2$ that are both antisymmetric and symplectic and show that they are not diagonalizable in $\mathbb{R}$.