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!

Finding eigenvectors for complex eigenvalues

  1. Apr 18, 2016 #1
    1. The problem statement, all variables and given/known data
    So I have been having trouble with finding the proper eigen vector for a complex eigen value
    for the matrix A=(-3 -5)
    . .........................(3 1)

    had a little trouble with formating this matrix sorry
    The eigen values are -1+i√11 and -1-i√11
    3. The attempt at a solution
    using AYY=0 (where Y is a vector (x, y) I obtain two different equations :
    3x+y-(-1+i√11)y=0 and -3x-5y-(-1+i√11)x=0

    these simplify too: 3x=(i√11 -2)y and 5y=(-2-i√11)x

    no I know that the right eigen vecotor is (i√11 -2,3) but why isnt (5, -2-i√11) one? they both work when I plug them in.
     
  2. jcsd
  3. Apr 18, 2016 #2

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    If ##\vec x## is an eigenvector of ##A## with eigenvalue ##\lambda##, then so is ##k \vec x##, where ##k \in \mathbb C, k\neq 0##.
    Check if ##(i\sqrt {11}-2,3)## is a (complex) scalar multiple of ##(5,-2-i\sqrt{11})##.
     
  4. Apr 18, 2016 #3
    well are you saying that both of these are eigen vectors for this matrix?
     
  5. Apr 18, 2016 #4
    They appear to be scalar multiples of each other
     
  6. Apr 18, 2016 #5

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    If they are non zero scalar multiples of each other, yes. As said, any non zero scalar multiple of an eigenvector is an eigenvector.
    Indeed. So either answer is correct.
     
  7. Apr 18, 2016 #6
    but when i try to compute the general solution it looks different.
     
  8. Apr 18, 2016 #7
    computing the general solution with eλt*V where V is the eigen vector
     
  9. Apr 18, 2016 #8

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    It may be me, but I don't understand what you are saying here.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding eigenvectors for complex eigenvalues
Loading...