本文印刷
全画面プリント
日仏数学拠点FJ-LMIセミナー
過去の記録 ～04/24｜次回の予定｜今後の予定 04/25～
| 担当者 | 小林俊行, ミカエル ペブズナー |
|---|
2026年04月28日(火)
16:00-17:00 数理科学研究科棟(駒場) 128号室
Khalid Koufany 氏 (Université de Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(英語)
https://fj-lmi.cnrs.fr/seminars/
Khalid Koufany 氏 (Université de Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(英語)
[ 講演概要 ]
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.
[ 講演参考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/
