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Ellipsoids – Quadratic Forms

Posts on the math of ellipsoids defined by quadratic forms

orthogonal projections of ellipsoid

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

In the mathematical section of this blog we deal with the geometry of Multivariate Normal Distributions [MVNs]. We found that the contour surfaces of MVNs are multidimensional ellipsoids given by quadratic forms of their constituting vectors. We have identified the variance-covariance matrix of a MVN as the inverse matrix mediating the required quadratic form. We also considered ellipsoidal cores of… Read More »Orthogonal projections of multidimensional ellipsoids – I – points on the ellipsoid that give us the surface points of the projection

Surfaces of n-dimensional ellipsoids – I – quadratic form and matrix equation

Multidimensional ellipsoids are mathematically interesting figures per se. But there is a reason why they sometimes also appear in the context of Machine Learning experiments. One reason is that Multivariate Normal Distributions [MND] often describe the statistical distributions of properties which characterize natural objects we investigate by ML-methods. And the locations of constant probability density of MNDs are surfaces of… Read More »Surfaces of n-dimensional ellipsoids – I – quadratic form and matrix equation