We assume that there exists a symplectic form $\omega$ on $\mathbb { R } ^ { n }$ with associated matrix $\Omega$ that is antisymmetric and invertible. Conclude that the integer $n$ is even.
We assume that there exists a symplectic form $\omega$ on $\mathbb { R } ^ { n }$ with associated matrix $\Omega$ that is antisymmetric and invertible. Conclude that the integer $n$ is even.