If $M \in \mathcal{S}_{n}(\mathbb{R})$, express $s^{\downarrow}(-M)$ as a function of the coordinates $\left(m_{1}, \ldots, m_{n}\right)$ of $s^{\downarrow}(M)$.
If $M \in \mathcal{S}_{n}(\mathbb{R})$, express $s^{\downarrow}(-M)$ as a function of the coordinates $\left(m_{1}, \ldots, m_{n}\right)$ of $s^{\downarrow}(M)$.