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Matrix, eigenvalues and diagonalization

  1. Dec 18, 2008 #1
    Matrix A= 1 2 0
    2 1 0
    2 -1 3

    i got eigenvalues k=3 k=-1 what do i do after that to prove it is not able to be diagonalized
  2. jcsd
  3. Dec 18, 2008 #2
  4. Dec 19, 2008 #3


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    Science Advisor
    Homework Helper

    Hi jkeatin! :smile:

    -1 is a is a double eigenvalue …

    so just plug -1 in and solve, and show that there is only one independent solution. :wink:
  5. Dec 19, 2008 #4


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    Re: eigenvectors

    The point is that an n by n matrix is diagonalizable if and only if it has n independent eigenvectors. Since -1 is a double root of the characteristic polynomial, the matrix may not have two independent eigenvectors corresponding to eigenvalue -1. That is what you need to prove.
  6. Dec 19, 2008 #5
    Re: eigenvectors

    thanks guys, got it!
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