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.