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!

Homework Help: 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


    User Avatar
    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


    User Avatar
    Science Advisor

    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook