Calculating orientation of ellipse from eigen values and eigen vectors

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Niraj
Niraj 2013-9-30
评论： Matt J 2013-10-4
Hi, I have a covariance matrix and i can compute the eigen values and eigen vectors. but from these information, i am unable to formulate an ellipse. I am unable to calculate the orientation of the ellipse.Can any one help me in it and point out any good source of information for calculating the the orientation of ellipse.
Thanks
  2 个评论
Matt J
Matt J 2013-9-30
Don't the eigenvectors themselves already define the orientation of the ellipse? If not, what does?
Niraj
Niraj 2013-9-30
Yes, so correct me if i am wrong. If i need to look at the orientation of an ellipse(angle subtended by the major axis). Then i need to find the eigen vector corresponding to the max eigen value. Then the orientation would be the inverse of the tan of eigen vectors.If V represents the max eigen vector then the orientation would be
atan(V(2,1)/V(1,1))
Right?

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回答（1 个）

Matt J
Matt J 2013-9-30
I think the major axis corresponds to the minimum eigenvalue, and the better way to compute the angle would be
atan2(V(2),V(1))
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Niraj
Niraj 2013-10-4
Thanks for the answers, but Major axis goes with max eigenvalue.It worked for me! Thanks for replies.
Matt J
Matt J 2013-10-4
编辑：Matt J 2013-10-4
Because the ellipses you are talking about are supposed to be the isocontours of a Gaussian PDF? I can't imagine any other reason.

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