Rotation and translation of basis to remove cross terms

[cooev769]

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.

Thanks.

 

[Erland]

Look up diagonalization of quadratic forms.

 

[cooev769]

Thanks Erland, just what I was looking for. You are a scholar and a gentleman.