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Homework Help: Find the eigenvalues and eigenvectors for the matrix

  1. Jun 2, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the eigenvalues and eigenvectors for the matrix [{13,5},{2,4}]

    2. Relevant equations
    None

    3. The attempt at a solution
    Well eigenvalues is easy, and turn out to be 14 and 3.
    So using eigenvalue 3, the two equations 10x1 + 5x2=0 and 2x1 + x2=0. Using these, I assumed the eigenvector to be [1,-2] but after putting it into Wolfram (or mathematica) it gives out the vector should be [-1,2]. Is there a difference? How should you discern between the two if not and where have I gone wrong if there is?
     
  2. jcsd
  3. Jun 2, 2010 #2

    Mark44

    Staff: Mentor

    Re: Eigenvectors

    Assuming your work is correct, there is no difference between <1, -2> and <-1, 2> as far as being eigenvectors. Each of these vectors is the -1 multiple of the other, so they are both in the same eigenspace, a subspace of dimension 1 (a line) in R2.
     
  4. Jun 2, 2010 #3
    Re: Eigenvectors

    Great. So do programs like mathematica choose them at random or is there a reason it chose <-1,2> over <1,-2>?
     
  5. Jun 2, 2010 #4

    Mark44

    Staff: Mentor

    Re: Eigenvectors

    I have no idea.
     
  6. Jun 2, 2010 #5
    Re: Eigenvectors

    Ok, thanks for the help!
     
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