Let $(V,\omega)$ be a symplectic vector space of dimension $2n$. How can I show that for an isotropic subspace $S \subset V$, there exists a symplectic basis $(A_i,B_i)$ for $V$ such that $S= $ span$(A_1,...,A_k)$ for some $k$.
It is related to this thread. I understand the symplectic case, but I cannot apply it to isotropic case.