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I know how to project a 3d ellipsoid onto a plane (e.g: Projection of ellipsoid).

I was wondering if there was some way of projecting onto the coordinate planes, an $n$-dimensional hyperellipsoid of the form $z^TCz = k$, where $z$ is a vector of $n$ coordinates, $C$ is an $n$x$n$ symmetric positive definite matrix and $k$ is a positive constant.

J. Doe
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  • What sort of projection do you have in mind? – amd Aug 29 '17 at 22:07
  • Good question. So for 2d ellipsoids, the projections that I am interested in are the projections obtained by cutting the coordinate axes with horizontal and vertical tangents to the ellipsoids. For 3d ellipsoids, I would use tangent planes. I am looking for an n-dimensional analog of that. I am not sure how to go about it though. – J. Doe Aug 29 '17 at 23:03

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