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: Complex Eigenvalues/vectors

  1. Nov 26, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the eigenvalues and eigenvectors of A. (Both eigenvalues and eigenvectors are now allowed
    to be complex.) Is it diagonalizable? Explain why or why not. If it is diagonalizable, explicitly
    find matrices P and D such that
    A = PDP−1
    where D is a diagonal 2 × 2 matrix.

    A = [ 0 -i | i 0 ]

    3. The attempt at a solution

    I determined that A cannot be diagonalized because, by the characteristic polynomial equation we get [tex]\lambda[/tex]2 + 1 = 0

    Therefore [tex]\lambda[/tex]1 = -i [tex]\lambda[/tex]2 = i

    plugging [tex]\lambda[/tex]2 into my matrix A I get:

    ix + iy = 0
    -ix + iy = 0

    but the only solution to this is x=y=0, I get the same result for [tex]\lambda[/tex]1

    Is this correct? I have a feeling this trivial solution is wrong
    I tried row reduction, but I still get the same result.
  2. jcsd
  3. Nov 26, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    so many minuses!

    Hi Iconate! :smile:

    (have a lambda: λ :wink:)
    Noooo! :redface:
  4. Nov 26, 2009 #3
    Re: so many minuses!

    Ahhh I see
    my determinant should be
    λ2 - (-i)(i) = 0
    λ2 + (i2) = 0
    λ2 - 1 = 0

    thus λ1 = 1 λ1 = -1

    Thanks >.<
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook