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Rotation and translation of basis to remove cross terms

  1. May 5, 2014 #1
    So in our notes we are given a general quadratic equation in three dimensions of the form:

    Ax^2 + By^2 + Cz^2 + Dxy + Eyz + Fxz + Gx + Hy + Iz + J = 0

    And then they say, by some rotation we can change this to the standard form:

    Ax^2 + By^2 + Cz^2 + J = 0

    The lecturer said don't worry about it you need to have done linear algebra to understand this. It turns out I have actually done linear algebra and am only doing this paper due to it being compulsory and a year behind. I've dealt with transformation of basis, linear independence etc. So if somebody could explain to me how they achieve this that would be good.

  2. jcsd
  3. May 6, 2014 #2


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    Science Advisor

    Look up diagonalization of quadratic forms.
  4. May 6, 2014 #3
    Thanks Erland, just what I was looking for. You are a scholar and a gentleman.
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