Show that $S _ { n } ^ { + } ( \mathbf { R } )$ and $S _ { n } ^ { + + } ( \mathbf { R } )$ are convex subsets of $M _ { n } ( \mathbf { R } )$. Are they vector subspaces of $M _ { n } ( \mathbf { R } )$ ?
Show that $S _ { n } ^ { + } ( \mathbf { R } )$ and $S _ { n } ^ { + + } ( \mathbf { R } )$ are convex subsets of $M _ { n } ( \mathbf { R } )$. Are they vector subspaces of $M _ { n } ( \mathbf { R } )$ ?