Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
We find an optimal upper bound on the volume of the John ellipsoid of a k-dimensional section of the n-dimensional cube, and an optimal lower bound on the volume of the Lowner ellipsoid of a projection of the n-dimensional cross-polytope onto a k-dimensional subspace, which are respectively (n/k)(k/2) and (k/n)(k/2) of the volume of the unit ball in R-k. Also, we describe all possible vectors in R-n, whose coordinates are the squared lengths of a projection of the standard basis in R-n onto a k-dimensional subspace.
Annalisa Buffa, Pablo Antolin Sanchez, Margarita Chasapi