Let $M _ { n } ( \mathbb { R } )$ be the space of $n \times n$ matrices with real entries, identified with the euclidean space $\mathbb { R } ^ { n ^ { 2 } }$. Let $X$ be a compact subset of $M _ { n } ( \mathbb { R } )$, and $S \subset \mathbb { C }$ be the set of all eigenvalues of the matrices in $X$. Show that $S$ is a compact subset of $\mathbb { C }$.