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Consider a matrix with coefficients in $\mathbb C$ . What is the condition for which the commutant of the matrix is equal to polynomials in the matrix?

I proved that if the matrix is diagonalisable then the commutant of the matrix is equal to polynomials in the matrix (I mean $C[M]$ ), but is this the necessary and sufficient condition? If yes how to prove the reciprocal?

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    $\begingroup$ By $C$ you mean complex numbers? What are "polynomials in the matrix"? I suggest you edit your title to something that gives the essence of the question. " challenging question by my teacher " doesn't do that. $\endgroup$ – R_D Nov 28 '16 at 2:28
  • $\begingroup$ Yes it means complex numbers , the subject was edited :) $\endgroup$ – AyoubAjarra Nov 28 '16 at 2:36
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    $\begingroup$ Maybe some punctuation...this insnt penelope. $\endgroup$ – Rene Schipperus Nov 28 '16 at 2:37
  • $\begingroup$ Look at this answer $\endgroup$ – A.Γ. Nov 28 '16 at 2:59
  • $\begingroup$ Thanks sir I guess I need to say that the matrix must be cyclic $\endgroup$ – AyoubAjarra Nov 28 '16 at 13:23

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