Re: Transforming expressions into ellipse normal form

From: Peter Spellucci (spellucci_at_fb04373.mathematik.tu-darmstadt.de)
Date: 03/22/05 

Date: Tue, 22 Mar 2005 10:53:01 +0000 (UTC)

In article <s2dv31lhdkdlvik7jmuvqtoe4laom1mdmk@4ax.com>,
 Roboy B <markieboy03@gmail.com> writes:
>How to transform the expression [3x^2-2xy+3y^2] by trigonometric
>method with coordinate transformation and matrix diagonalization
>method?

  this is [x y ][ 3 -1 ] [x]
                [-1 3 ] [y]
now compute the two eigenvalues of the 2 by 2 matrix with eigenvectors
normalized to euclidean length 1. Say

   U'*A*U = diag(lambda1,lambda2)
then
   A=U*diag(lambda1,lambda2)*U'
insert this above set [v,w]'=U'*[x,y]' , done . (.' is transposition)
hth
peter