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I Conics -- Matrix Decomposition

  1. May 18, 2017 #1
    I was reading about ellipse-ellipse intersection and I came across this article:

    https://math.stackexchange.com/ques...c-and-line-in-homogeneous-space/867428#867428

    I wrote a program that implements this method and it works, but now I'm working to understand why. I understand how [itex]D = L^T C L[/itex] is constructed, but I don't understand how/why the decomposition [itex]P=D+\lambda L[/itex] works. It seems that the author seems to be solving for one of the eigenvalues of D, but I don't immediately recognize if this is a standard method or not (i.e. it only works for conics, or only when decomposing from rank 2 to rank 1 matrices, etc). Any reference material or help understanding the theory here is greatly appreciated.
     
  2. jcsd
  3. May 23, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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