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Minimal polynomial, transpose, similar

  1. Apr 14, 2009 #1
    1. The problem statement, all variables and given/known data

    a) Prove that if a polynomial f(lambda) has f(A)=0, then f(AT)=0

    b) Prove that A and AT have the same minimal polynomial.

    c) If A has a cyclic vector, prove that AT is similar to A.


    2. The attempt at a solution

    a) I know that I need to show that f(AT) = f(A)T.

    b) The main problem is that I don't think I understand completely what the minimal polynomial is. I know how to get the minimal polynomial from the last column of a matrix in rational canonical form, and that's about it.

    c) This should be a direct consequence of part (b) since same minimal polynomial --> similar.
     
  2. jcsd
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