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Rational Canonical Form

  1. Mar 10, 2009 #1
    Hi, can someone show me how one would go about finding the matrix Q in Q^(-1) A Q = RationalCanonicalForm(A). Please demonstrate using the example

    {4, 1, 2, 0}
    {-4, 0, 1, 5} = A
    {0, 0, 1, -1}
    {0, 0, 1, 3}

    where the characteristic polynomial is (x-2)^4 and the minimal polynomial is (x-2)^3. To save you guys some time, I've computed

    {2, 1, 2, 0}
    {-4, -2, 1, 5} = (A-2I)
    {0, 0, -1, -1}
    {0, 0, 1, 1}

    {0, 0, 3, 3}
    {0, 0, -6, -6} = (A-2I)^2
    {0, 0, 0, 0}
    {0, 0, 0, 0}

    Thanks in advance guys!
     
  2. jcsd
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