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Affine-invariant orders on the set of positive-definite matrices

Mostajeran, C and Sepulchre, R (2017) Affine-invariant orders on the set of positive-definite matrices. In: 3rd conference on Geometric Science of Information (GSI), -- to -- pp. 613-620..

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© 2017, Springer International Publishing AG. We introduce a family of orders on the set S+n of positive-definite matrices of dimension n derived from the homogeneous geometry of S+n induced by the natural transitive action of the general linear group GL(n). The orders are induced by affine-invariant cone fields, which arise naturally from a local analysis of the orders that are compatible with the homogeneous structure of S+n. We then revisit the well-known Löwner-Heinz theorem and provide an extension of this classical result derived using differential positivity with respect to affine-invariant cone fields.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Divisions: Div F > Control
Depositing User: Unnamed user with email
Date Deposited: 08 Dec 2017 20:30
Last Modified: 09 Sep 2021 03:01
DOI: 10.1007/978-3-319-68445-1_71