6 citations · 23 across the 18 of their papers we have counts for
5 papers · 1 filter
Sharp Inequalities for Products of Principal Minors of Positive Definite Matrices
Tobias Boege, Ludovick Bouthat
We study sharp inequalities for ratios of products of principal minors of real positive definite matrices. Our main result gives a closed-form solution to a family of nonconvex opt…
On the Submultiplicativity of Matrix Norms Induced by Random Vectors
Ludovick Bouthat
In a recent article, Chávez, Garcia and Hurley introduced a new family of norms on the space of complex matrices which are induced by random…
On the Geometry of the Birkhoff Polytope. II. The Schatten -norms
Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin
In the first of this series of two articles, we studied some geometrical aspects of the Birkhoff polytope, the compact convex set of all doubly stochastic matrices, na…
On the Geometry of the Birkhoff Polytope. I. The operator -norms
Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin
The geometry of the Birkhoff polytope, i.e., the compact convex set of all doubly stochastic matrices, has been an active subject of research. While its faces, edges a…
On a question of Erdős on doubly stochastic matrices
Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin
In a celebrated paper of Marcus and Ree (1959), it was shown that if is an doubly stochastic matrix, then there is a permutation such that $\su…