# Using power of matrix to find JCF

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?

• 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. – amd Jun 9 at 20:36