## Rational Canonical Form of a Matrix

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}