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# Quadratic equation of 3 variables watch

1. Hi,

When you have quartic equation of three variables (i.e ax^2+by^2+cz^2*dxy+exz+fyz+g=0) I read that you can put it into matrix form A such that XAX^T=0

Where X is (x,y,z,1)

Now why is this form useful?
What can A tell you about the equation?

I have a feeling Gauss Jordan and determinants could come in handy for simplifying the equation, and classifying it as a surface

Any ideas?
2. (Original post by number23)
Hi,

When you have quartic equation of three variables (i.e ax^2+by^2+cz^2*dxy+exz+fyz+g=0) I read that you can put it into matrix form A such that XAX^T=0

Where X is (x,y,z,1)

Now why is this form useful?
What can A tell you about the equation?

I have a feeling Gauss Jordan and determinants could come in handy for simplifying the equation, and classifying it as a surface

Any ideas?
I do not remember much about this topic but I would imagine this is all about diagonalization of "3 D conics"

this form allows you to rotate them in order to see what type they are
e.g ellipsoids, paraboloids, hyperboloids (or the degenerate case of the pair of lines in 3D i.e a double cone)

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