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Can one figure out if a matrix is cyclic just by looking at its Jordan Normal Form ?

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  • $\begingroup$ What is a cyclic matrix? Do you mean circulant? $\endgroup$ Sep 12, 2017 at 8:50
  • $\begingroup$ @DietrichBurde yes $\endgroup$
    – macco
    Sep 12, 2017 at 8:53
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    $\begingroup$ The answer is no. A non-circulant matrix can be similar to a circulant matrix, but both matrices have the same Jordan forms due to similarity. $\endgroup$
    – user1551
    Sep 12, 2017 at 9:22
  • $\begingroup$ On the other hand, you can tell whether $\Bbb C^n$ is $T$-cyclic by looking at the Jordan form. $\endgroup$ Sep 12, 2017 at 11:55

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