Talk:Matrix representation of conic sections
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My question is this,
"what do the eigenlines of a conic's assosiated matrix correspond to, and why?"
The ellipse 17x^2 + 12xy +8y^2 = 1
may be assosiated with (x,y) (17 6) (x)
(6 8) (y)
having eigenvectors a(1,-2) and b (2,1).
My understanding of eigenvectors are that they are vectors that are not changed when transformed by the matrix.
I'm guessing there's a relationship between the focus and directrix of a conic and its eigenlines. But I can't seem to find out what that relationship is anywhere.
I'm not good enough at sums to figure it out for myself, so if you can explain this I'd be most pleased.
The eigenvectors provide the axis of the conic, or the ellipse in your case. What I find puzzling is that the matrix associated with the conic is 3x3, so you actually get 3 eigenvectors. Presumably you take the two with the largest eigenvalues or something similar. This part of the page is not very clear. Aether1999 13:11, 6 April 2007 (UTC)
My answer to you is: I believe that he is obaining the eigenvalues of the A11 matrix, not the original A matrix. I am trying to work the exact values of the center, vertices, Axes. —Preceding unsigned comment added by 68.9.67.188 (talk) 00:22, 12 May 2008 (UTC)
[edit] Need Help
I need help phrasing a certain part of the page. Under the section Axes it says: eigenvector of A, when it should say: eigenvector of A11. I was going to fix it myself but, what I thought would work didn't and I can't figure out a way to make it work. Please help.--SurrealWarrior 01:32, 20 June 2007 (UTC)
I understand what you are saying here. The article indicates that eigenvectors give the prinicpal axes. However, the equations that the eigenvectors gives, first of all, are not perpendicular, and second, are 2 lines through the origin. So, they can't be the axes. I will work some more on it. Input is appreciated. —Preceding unsigned comment added by 158.123.55.4 (talk) 13:10, 14 May 2008 (UTC)
