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Linear algebra: cyclic vector space

  1. Nov 17, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove that V is cyclic relative to a linear transformation T, T:V->V if and only if the minimal polynomial of T is the same as the characteristic polynomial of T.


    2. Relevant equations



    3. The attempt at a solution

    i have finished the => direction (proved that if V is cyclic, mini poly = char poly). i have absolutely no clue where to even start with the other direction. any help would be appreciated.

    thanks,

    cj.
     
  2. jcsd
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