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Linear algebra find the minimal polynomial

  1. Jan 30, 2014 #1
    1. The problem statement, all variables and given/known data
    M: V -> V linear operator st M^2 + 1_v = 0
    find the POSSIBILITIES for min. pol. of M^3+2M^2+M+3I_v


    2. Relevant equations



    3. The attempt at a solution

    using M^2 = -1_v,
    i rewrote the operator(?) as
    M^3 + M + I_v

    i dunno what to do. i guessed min poly to be like x^3-x-1
    but what would be other possibilities. i seriously doubt the one i guessed is even correct.

    i know that, if min poly is u(x) then u(M) = 0.
     
  2. jcsd
  3. Jan 30, 2014 #2

    Dick

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    Science Advisor
    Homework Helper

    M^3=(-M), isn't it?
     
  4. Jan 31, 2014 #3
    got it.
     
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