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Quadratic surfaces + principle axes

  1. Sep 28, 2011 #1
    In my lecture notes, one of the example problems involving a quadratic surface uses the
    following method to generate the principle axes


    Q.(1,0,0)^T for the x-axis

    Q.(0,1,0^T for the y-axis

    Q.(0,0,1)^T for the z-axis

    note Q is a 3x3 orthogonal matrix (which im assuming contains the eigenvectors of the original 3x3 matrix)

    To give this some reasoning, do we do Q.(1,0,0)^T to find principle x-axis since x is what we are only interested in (which explains the multiplication of Q by (1,0,0)^T )?

    Likewise does this same logic work in the case of the principal y and z-axis ?

    thanks
     
  2. jcsd
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