1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding eigenvalues to use in Cayley-Hamilton theorem problem

  1. Oct 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Let C =


    Use the Cayley-Hamilton theorem to compute C^3.

    2. Relevant equations

    Cayley-Hamilton theorem says that every square matrix satisfies its own characteristic equation.


    where P is the matrix formed from linearly independant eigenvectors of C and D is the diagonal matrix formed from the eigenvalues of C.

    3. The attempt at a solution

    I get the characteristic equation of C is

    [itex]\lambda^3 - 2\lambda^2 - \lambda - 2 = 0 [/itex]

    I get stuck because I can't factorise this and get the eigenvalues to proceed. Is there some trick to factorising cubics like this?
  2. jcsd
  3. Oct 28, 2012 #2

    Attached Files:

    • 001.jpg
      File size:
      12.8 KB
  4. Oct 28, 2012 #3
    Thanks, I was just going back over the lecture notes and realized that I was absurdly confused in that section (I'm embarassed I even asked this question!)...anyway, I get it now, thanks for that :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Finding eigenvalues to use in Cayley-Hamilton theorem problem