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Homework Help: Linear Algebra - Cyclic Decomposition

  1. May 9, 2010 #1
    Linear Algebra - Cyclic Decomposition, Rational Canonical Form

    1. The problem statement, all variables and given/known data
    I am given a 5x5 real matrix A, and I am looking for an invertible matrix P so that [tex]P^{-1}AP[/tex] is in rational form.

    2. Relevant equations

    3. The attempt at a solution
    I calculated the characteristic polynomial and minimal polynomial, and they are the same in this case. There is only 1 eigenvalue, and my minimal polynomial is of the form [tex]p(x)=p_1p_2p_3[/tex] where [tex]p_i[/tex] are relatively prime polynomials. I can compute companion matrices so I know what the rational form looks like, but I am stumped on how to obtain that matrix P. Any pointers are appreciated.
    Last edited: May 9, 2010
  2. jcsd
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