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elliptic paraboloid

Quadratic form functions as graph functions – I – level sets and gradients

The last months I have seldom written posts in this blog. The reason is that I am occupied with a book about “The geometry of Multivariate Normal Distributions”. Which will cover a lot more topics than the ones discussed in this blog so far. One of those topics is the use of quadratic form functions as graph functions to produce… Read More »Quadratic form functions as graph functions – I – level sets and gradients

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