Affine-invariant orders on the set of positive-definite matrices
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Authors
Mostajeran, C
Sepulchre, R
Publication Date
2017-11-01Journal Title
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Conference Name
3rd conference on Geometric Science of Information (GSI)
ISSN
0302-9743
ISBN
9783319684444
Publisher
Springer International Publishing
Volume
10589 LNCS
Pages
613-620
Language
English
Type
Conference Object
This Version
AM
Metadata
Show full item recordCitation
Mostajeran, C., & Sepulchre, R. (2017). Affine-invariant orders on the set of positive-definite matrices. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 10589 LNCS 613-620. https://doi.org/10.1007/978-3-319-68445-1_71
Abstract
© 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.
Sponsorship
ERC
Funder references
European Research Council (670645)
EPSRC (1355845)
Identifiers
External DOI: https://doi.org/10.1007/978-3-319-68445-1_71
This record's URL: https://www.repository.cam.ac.uk/handle/1810/294314
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http://www.rioxx.net/licenses/all-rights-reserved
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