We equip the space $\mathcal { M } _ { n } ( \mathbb { R } )$ with its topology as a normed vector space. Show that the symplectic group $\mathrm { Sp } _ { n } ( \mathbb { R } )$ is an arc-connected subset of this space.
We equip the space $\mathcal { M } _ { n } ( \mathbb { R } )$ with its topology as a normed vector space. Show that the symplectic group $\mathrm { Sp } _ { n } ( \mathbb { R } )$ is an arc-connected subset of this space.