Affine-Invariant Orders on the Set of Positive-Defi nite Matrices

07/11/2017
Publication GSI2017
OAI : oai:www.see.asso.fr:17410:22526
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Résumé

We introduce a family of orders on the set S+of positive definite matrices of dimension n derived from the homogeneous geometry of S+induced by the natural transitive action of the general linear group GL(n). The orders are induced by affne-invariant cone fields, which arise naturally from a local analysis of the orders that are compatible with the homogeneous structure of S+. We then revisit the well-known Löwner-Heinz theorem and provide an extension of this classical result derived using differential positivity with respect to affne-invariant cone elds.

Affine-Invariant Orders on the Set of Positive-Definite Matrices

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application/pdf Affine-Invariant Orders on the Set of Positive-Defi nite Matrices Cyrus Mostajeran, Rodolphe Sepulchre
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contenu protégé  Document accessible sous conditions - vous devez vous connecter ou vous enregistrer pour accéder à ou acquérir ce document.
- Accès libre pour les ayants-droit

We introduce a family of orders on the set S+of positive definite matrices of dimension n derived from the homogeneous geometry of S+induced by the natural transitive action of the general linear group GL(n). The orders are induced by affne-invariant cone fields, which arise naturally from a local analysis of the orders that are compatible with the homogeneous structure of S+. We then revisit the well-known Löwner-Heinz theorem and provide an extension of this classical result derived using differential positivity with respect to affne-invariant cone elds.
Affine-Invariant Orders on the Set of Positive-Definite Matrices
application/pdf Affine-Invariant Orders on the Set of Positive-Defi nite Matrices (slides)

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