1. Not finding help here? Sign up for a free 30min 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 eigenvector from eigenvalue

  1. Mar 20, 2009 #1
    1. The problem statement, all variables and given/known data
    For the matrix A =

    -1, 5
    -2, -3

    I found the eigenvalues to be -2 + 3i and -2 - 3i.
    Now I need some help to find the eigenvectors corresponding to each.

    2. Relevant equations



    3. The attempt at a solution
    For r = -2 + 3i, I plugged that into the (A - Ir) matrix, which I found to be

    1-3i, 5
    -2, -1-3i

    I multiply that matrix with the vector (x y) and set it equal to (0 0) right? If I do that I get the following 2 equations:

    (1-3i)x + 5y = 0
    -2x - (-1-3i)y = 0

    Did I make a mistake somewhere, or how should I go on to find the eigenvector? Thanks!
     
  2. jcsd
  3. Mar 20, 2009 #2
    Looks good to me so far, I haven't checked the actual numbers but the principles are fine.

    Edit:Checked the numbers and they look fine too.
     
  4. Mar 20, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I prefer just to use the basic definition of "eigenvalue". If [itex]\lambda[/itex] is and eigenvalue of A then there exist a non-zero vector v such that [itex]Av= \lambda v[/itex] and, of course, v is an eigenvector.

    Here, for [itex]\lambda= -2+ 3}[/itex] that is
    [tex]A= \begin{bmatrix}-1 & 5 \\ -2 & -3\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}= \begin{bmatrix}(-2+i\sqrt{3})x \\ (-2+3i)\end{bmatrix}[/tex]
    which reduces to two equations:
    [itex]-x+ 5y= (-2+ 3i)x[/itex] and [itex]-2x- 3y= (-2+ 3i)y[/itex] both of which reduce to 5y= (-1+ 3i)x. Taking x= 5, y= -1+ 3i satisfies that and gives (5, -1+ 3i) as an eigenvector corresponding to eigenvalue -2+ 3i. A similar calculation gives an eigenvector corresponding to eigenvalue -2- 3i.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding eigenvector from eigenvalue
Loading...