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Matrix canonical form

  1. Oct 30, 2011 #1
    1. The problem statement, all variables and given/known data
    Given the invariant factors of the matrix λI - A are
    d1 to d5 = 1, d6 = (λ-3)(λ-2)2 , d7 = (λ-3)2(λ-2)2

    Display the rational canonical form of A
    Display the Jordan canonical form of A

    3. The attempt at a solution
    I'm half guessing here, but we have for d6 : λ3 - 7λ2 + 16λ - 12
    and for d7 : λ4 - 10λ3 + 13λ2 + 12λ + 36
    Would the rational canonical form be a diagonal block matrix (sorry for the formatting)
    A | 0
    0 | B
    with A =
    0 0 12
    1 0 -16
    0 1 7
    and B =
    0 0 0 -36
    1 0 0 -12
    0 1 0 -13
    0 0 1 10

    or would it be a 7x7 block matrix with the first 5 diagonals = [1]?

    For the Jordan form I just need to find the eigenvectors and put them in the same block matrix form, right?
     
  2. jcsd
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