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n-dimensional ellipsoids

orthogonal projections of ellipsoid

Orthogonal projections of multidimensional ellipsoids – I – points on the ellipsoid that give us the surface points of the projection

A reader of a parallel post-series on n-ellipsoids has asked me how I could know what the matrix for the quadratic form of the orthogonal projection of a (n-1) dimensional-ellipsoid onto a (n-1)-dimensional sub-space of the ℝn looks like. I had stated in previous posts that we can directly derive the elements of the matrix describing projections of ellipsoids or… Read More »Orthogonal projections of multidimensional ellipsoids – I – points on the ellipsoid that give us the surface points of the projection

n-dimensional spheres and ellipsoids – III – Surface area of n-dimensional ellipsoid and its relation to MVN-statistics

In the 2nd post of this series we have derived an explicit formula for the volume of a n-dimensional ellipsoid (in an Euclidean space). One reason for the relatively simple derivation was that the determinant of the generating linear transformation could be taken in front of the volume integral. Unfortunately, an analogue sequence of steps is not possible for an… Read More »n-dimensional spheres and ellipsoids – III – Surface area of n-dimensional ellipsoid and its relation to MVN-statistics