Let $C\in \text{Mat}_{n\times n}(\mathbb R)$. Then which of the alternatives are correct:
- $\operatorname{dim}\langle I,C,C^2,\dots,C^{2n}\rangle$ is at most $2n$
- $\operatorname{dim} \langle I,C,C^2,\dots,C^{2n}\rangle$ is at most $n$.
Let $C\in \text{Mat}_{n\times n}(\mathbb R)$. Then which of the alternatives are correct: