Show that for all matrices $A$ and $B$ in $\operatorname{Sym}^+(p)$ and all non-negative real numbers $a$ and $b$, we have $aA + bB \in \operatorname{Sym}^+(p)$.
Show that for all matrices $A$ and $B$ in $\operatorname{Sym}^+(p)$ and all non-negative real numbers $a$ and $b$, we have $aA + bB \in \operatorname{Sym}^+(p)$.