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Homework Help: Finding eigen values of a 2x2 matrix

  1. Apr 12, 2010 #1
    Find the eigenvalues of the following 2x2 matrix:

    (0 1)/(-1 0)

    2. Relevant equations

    By using the forumla (a-λ)(d-λ) -bc I was able to obtain the following:

    λ^(2) + 1 = 0
    λ^(2) = -1

    λ = ± √ (-1)

    Is thos correct? Also what relevance does this have on the fixed points?
  2. jcsd
  3. Apr 12, 2010 #2


    Staff: Mentor

    Yes, they are correct. You can also write them as λ = ±i.

    Regarding fixed points, you might be talking about this: For some vectors x1 and x2, Ax1 = ix1, and Ax2 =- ix2, where A is your matrix. i and -i are the eigenvalues and the x vectors are eigenvectors.
  4. Apr 12, 2010 #3
    Thanks for that just needed some confirmation:)

    I was just reading that if a system has eigen values of i and -i then this corresponds to a 90 degree planar rotation?

    I ask because the question im answering goes on to say.

    Use eigen value analysis to dscribe the behaviour of the system.

    Any help would be great
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