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Diagonalizing hermitian matrices - how to get eigenvectors after finding eigenvalues?

  1. Jul 27, 2012 #1
    1. The problem statement, all variables and given/known data
    I can find my eigenvalues just fine, and they're both real, as expected. My first eigenvalue is -3, which I know is correct.

    I have the equations 5x+(3-i)y=0, (3+i)x+2y=0

    Both of the equations come from my hermitian matrix, after I substituted λ=-3.

    2. Relevant equations



    3. The attempt at a solution

    I have absolutely no idea how to solve this. This case is simple enough to be solved by trial and error, but how would I proceed if I had harder equations?

    I can't use both equations since I get x=x or y=y if I substitute one into the other, since they're both the same equation.
     
  2. jcsd
  3. Jul 27, 2012 #2
    Re: Diagonalizing hermitian matrices - how to get eigenvectors after finding eigenval

    Nevermind, doing another (easier) exercise allowed me to see that I only have to set ax = by, and force a value to either x or y.
     
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