Given a $5 \times 5$ matrix $A$, find any Jordan canonical form for $A$.

There is a hint, that you should calculate $A^3$ first (crucially, not $(A-\lambda E_5)^3$). What information does the power of $A$ give me, which I can then use to find a JCF?

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    $\begingroup$ Without seeing the specific matrix that you’re working with, it’s impossible to say, but $A^3$ might give you some clues about the minimal polynomial, which in turn restricts the possible JNFs. $\endgroup$ – amd Jun 9 at 20:36

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