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I'm trying to find the characteristic polynomial of an nxn nilpotent matrix with complex coefficients. I understand how to do it with standard coefficients but I'm a bit confused as to how to proceed with complex coefficients.

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it is $$ x^n $$ while the minimal polynomial is some $x^k$ with $1 \leq k \leq n,$ unless your matrix is the zero matrix

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  • $\begingroup$ I just want to confirm, does this still apply with complex coefficients? $\endgroup$
    – ChumBot
    Apr 10 '20 at 20:54
  • $\begingroup$ yes........................................................ $\endgroup$
    – Will Jagy
    Apr 10 '20 at 20:55
  • $\begingroup$ This actually applies to matrices over any field. $\endgroup$
    – Bernard
    Apr 10 '20 at 22:22

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