Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Primary decomposition theorem

  1. Dec 14, 2011 #1
    Let F= R or C, and A =
    [1 2 3] is considered as linear operator in F3
    [0 1 2]
    [0 0 1]
    then the minimal polynomial of A = (x-1)^3, can we say that the primary decomposition thm doesn't give any decomposition, can we find an invertible P s.t P^-1*A*p is a block diagonal matrix?
  2. jcsd
  3. Dec 18, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    it seems 1 is the only eigenvalue. now look for the eigenvectors with that eigenvalue. how many do you find? is that enough to diagonalize the matrix?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook