Recall why $\mathcal{S}_{n}(\mathbb{R})$ is a real vector space and what is its dimension. Why is the map $s^{\downarrow}$ well-defined on $\mathcal{S}_{n}(\mathbb{R})$?
Recall why $\mathcal{S}_{n}(\mathbb{R})$ is a real vector space and what is its dimension. Why is the map $s^{\downarrow}$ well-defined on $\mathcal{S}_{n}(\mathbb{R})$?