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If $f(x)$ is minimal polynomial of the $4\times 4$ matrix A=\begin{pmatrix} 0 &0 &0& 1\\ 1 &0 &0 &0\\ 0 &1 &0 &0\\ 0 &0 &1 &0 \end{pmatrix}

Then what is rank of $f(A)$? I think $f(A)$ will be a zero matrix so its rank is 0. Am I right?

  • 15
    Yes, that's exactly right.2012-12-24

2 Answers 2

2

Yes, that's exactly right... $\phantom{ok I'll add a little random text here to avoid automatic conversion}{}{}$