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
Some of my readers know that I am presently writing a book about Multivariate Normal distributions and related geometric properties of their level sets (multidimensional ellipsoids). For certain topics of the book, I sometimes use the latest free edition of ChatGPT to verify some claims and to get a list of respective papers. Sometimes also for a proof … However,… Read More »Getting the semi-axes of an ellipse by differentiation of its graph functions – a simple step for a human, but not for ChatGPT 5.x ….
This post series covers the topic of orthogonal projections of ellipsoids from their embedding multidimensional space down to sub-spaces. In this post we will verify some of our mathematical results by a numerical experiment: We will compute the projections of an ellipsoid from its embedding 4-dimensional (Euclidean) space down to 3- and 2-dimensional sub-spaces. We will check with the help… Read More »Orthogonal projections of multidimensional ellipsoids – VII – experimental checks of projections from a 4-dimensional space to sub-spaces
After our recent excursion to Schur complements, some readers may wish to get a visual confirmation of our rather theoretical results. As usual in this blog, we will perform some numerical experiments. To get started, I will restrict my efforts to the projection of an ellipsoid from a 4-dimensional Euclidean space down to three- and two-dimensional sub-spaces. In a later… Read More »Orthogonal projections of multidimensional ellipsoids – VI – considerations and vector generation for numerical experiments in four dimensions