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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

    mathwonk

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    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?
     
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