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I would just like to make sure I understand the uniqueness part correctly. Suppose I know that the Jordan blocks $J_1, ..., J_n$ make up the Jordan form of $A$. Then I can arrange the blocks $J_1, ..., J_n$ in any order on the diagonal and still have a Jordan form of $A$? Furthermore, there exists no other set of Jordan blocks $J_1, ..., J_k$ such that $A$ is similar to a block diagonal matrix constructed from $J_1, ..., J_k$?

Thank you.

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Yes the understanding is correct. Jordan form is unique up to permutation of blocks

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  • $\begingroup$ Thank you ${}{}$ $\endgroup$
    – Ovi
    Commented Oct 17, 2018 at 15:58

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