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Reflection matrix

  1. Apr 13, 2009 #1
    1. The problem statement, all variables and given/known data
    Given the matrix A=
    -1/2 root(3)/2
    root(3)/2 1/2

    determine if the matrix is a rotation about the origin or a reflection about the positive x axis
    and find the angle between the that the line makes with the x-axis



    2. Relevant equations



    3. The attempt at a solution

    I found the det(A)=-1 can I concluded that the matrix reflects vectors?
    and also how do you find the angle?
    I tried doing projection onto the axis. but didnt get me anywhere
    please help..
     
  2. jcsd
  3. Apr 14, 2009 #2

    tiny-tim

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    Hi Lchan1! :smile:

    (have a square-root: √ :wink:)
    Yup! :smile:
    learn this:

    rotation through angle θ is

    cosθ sinθ
    -sinθ cosθ :wink:
     
  4. Apr 14, 2009 #3
    does that mean it's a rotation and a reflection?
    pi/3 will be the angle?
     
  5. Apr 14, 2009 #4

    tiny-tim

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    sorry, I was a bit too cryptic last time :redface:

    a combination of a rotation and a reflection is a reflection …

    it would have been better if I'd said

    rotation through angle θ is

    cosθ sinθ
    -sinθ cosθ

    reflection about y-axis is

    -1 0
    0 1

    and if you combine them you get … ? :smile:
     
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