Let $\mathcal{R}$ be a valuation ring, and consider an $\mathcal{R}$-linear endomorphism $L:\mathcal{R}^{n}\rightarrow \mathcal{R}^{n}$. Is there any criterion for telling when $L$ can be diagonalized? I would be specially interested in the case where $L$ is an automorphism and $\mathcal{R}$ is the valuation ring associated to a complete non-archimedean field.