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Linear algebra rotation

  1. Jan 27, 2013 #1
    hi,
    I understand how to do the rotation equation

    A = [ cosθ -sinθ
    sinθ cosθ]

    A*v = [ cosθ -sinθ * [ x = [ xcosθ - ysinθ
    sinθ cosθ] y ] xsinθ + ycosθ ]

    A*v = [ cos90 -sin90 * [ 6
    sin90 cos90 ] 4 ]

    = [ 0, -1 * [ 6 = [ 0 * 6 - 1 * 4 = [ -4
    1, 0 ] 4 ] 1 * 6 + 0 * 4 ] 6 ]

    but the text book I am using doesn't go into using different angle as you can see this is a 90 degree equation but what if I wanted to use 30 degrees or 5 degree instead.I have look on the internet for some advice but don't seem to be able to find some?
     
  2. jcsd
  3. Jan 27, 2013 #2

    Simon Bridge

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    What's wrong with just putting the different angle in for theta?
    http://en.wikipedia.org/wiki/Rotation_matrix

    eg. to rotate 30 degrees, sin(30)=1/2 and cos(30)=√3/2 so the matrix becomes:

    $$\mathbf{A}=\left ( \begin{array}{cc}
    \sqrt{3}/2 & -1/2 \\ 1/2 & \sqrt{3}/2
    \end{array}\right )$$

    I'm unsure about your notation though.
     
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