Find all possible Jordan Canonical forms of a nilpotent $3\times 3$ matrix. How do I go about doing this?
2026-03-25 19:25:26.1774466726
All possible Jordan Canonical forms of a nilpotent $3\times 3$ matrix
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Hint: Note (or show) that a matrix is nilpotent if and only if its only eigenvalue is $0$. If you're proving this, it helps to use the Cayley-Hamilton theorem.