Show that the product of two symplectic matrices is a symplectic matrix. Is the set $\mathrm{Sp}_{2n}(\mathbb{R})$ a vector subspace of $\mathcal{M}_{2n}(\mathbb{R})$?
Show that the product of two symplectic matrices is a symplectic matrix. Is the set $\mathrm{Sp}_{2n}(\mathbb{R})$ a vector subspace of $\mathcal{M}_{2n}(\mathbb{R})$?