Prove Theorem 2: Let $M \in \mathscr { D } _ { \rho } \left( S _ { n } ( \mathbb { R } ) \right)$. Then there exists $r \in \mathbb { R } _ { + } ^ { * }$ such that $r \leqslant \rho$ and an orthogonal matrix $P \in \mathscr { D } _ { r } \left( \mathscr { M } _ { n } ( \mathbb { R } ) \right)$ such that $P ^ { \mathrm { T } } \cdot M \cdot P$ is diagonal.