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Linear Trans. Rotations

  1. May 6, 2007 #1
    Derive the matrix for the transformation that rotates a point (x,y,z) counterclockwise about the y-axis through an angle (X).

    My book gives me a matrice for the y-axis move.

    (cosX 0 sinX)
    (0 1 0 )
    (-sinX 0 cosX)

    call the above matrix [A]

    Im also given this formula for a unit vector

    cos(V)i + cos(W)j + cos(Y)k

    The way that I see the question, is that I need to somehow derive matix [A]
    from the given unit vector formula.

    I just dont see exactly how they are connected here.

    I really DON'T want the solution for this, just some insight maby on the connection between the formula and the matrix.

    I know that if I have a vector u and an angle (X) I can just multiply
    Au to get the rotated vector. So I do know how to use the matrix.
  2. jcsd
  3. May 6, 2007 #2
    The formula can be written as a matrix vector (cos(V) cos(W) cos(Y))^T.

    You are really looking for the linear transformation matrix such that L(x,y,z) rotates the standard basis for lR^3 by an angle X.
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