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FJ-LMI Seminar
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Organizer(s) | Toshiyuki Kobayashi, Michael Pevzner |
|---|
2026/04/28
16:00-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Joint with Lie groups and Representation theory seminar
Khalid Koufany (Université de Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(英語)
https://fj-lmi.cnrs.fr/seminars/
Joint with Lie groups and Representation theory seminar
Khalid Koufany (Université de Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(英語)
[ Abstract ]
This talk starts from a simple question: how can one define a geometric mean for sparse positive definite matrices without destroying their zero pattern?
For the arrowhead pattern, this leads naturally to the five-dimensional Vinberg cone, a basic non-symmetric homogeneous cone.
I will present two intrinsic means on this cone: a Cholesky-Vinberg mean built from triangular Cholesky factors, and a logarithmic Vinberg mean built from global clan (Vinberg algebra) coordinates.
The first is tied to a flat affine geometry with torsion, while the second belongs to a torsion-free flat geometry.
I will also explain why these means differ from the classical Riemannian midpoint and why this difference is a genuinely non-symmetric phenomenon.
If time permits, I will give an application to quantum information theory.
[ Reference URL ]This talk starts from a simple question: how can one define a geometric mean for sparse positive definite matrices without destroying their zero pattern?
For the arrowhead pattern, this leads naturally to the five-dimensional Vinberg cone, a basic non-symmetric homogeneous cone.
I will present two intrinsic means on this cone: a Cholesky-Vinberg mean built from triangular Cholesky factors, and a logarithmic Vinberg mean built from global clan (Vinberg algebra) coordinates.
The first is tied to a flat affine geometry with torsion, while the second belongs to a torsion-free flat geometry.
I will also explain why these means differ from the classical Riemannian midpoint and why this difference is a genuinely non-symmetric phenomenon.
If time permits, I will give an application to quantum information theory.
https://fj-lmi.cnrs.fr/seminars/
