Homework Help: Linear Algebra - Cyclic Decomposition

1. May 9, 2010

Leitmotif

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 $$P^{-1}AP$$ 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 $$p(x)=p_1p_2p_3$$ where $$p_i$$ 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