Published September 2018
| Submitted
Journal Article
Open
Simplicial Faces of the Set of Correlation Matrices
- Creators
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Tropp, Joel A.
Abstract
This paper concerns the facial geometry of the set of n×n correlation matrices. The main result states that almost every set of r vertices generates a simplicial face, provided that r ≤ √cn, where c is an absolute constant. This bound is qualitatively sharp because the set of correlation matrices has no simplicial face generated by more than √2n vertices.
Additional Information
© Springer Science+Business Media, LLC, part of Springer Nature 2017. Received: 5 December 2016 / Revised: 10 November 2017 / Accepted: 15 December 2017. The author thanks Richard Küng and Benjamin Recht for helpful conversations related to this work. This research was partially supported by ONR award N00014-11-1002 and the Gordon & Betty Moore Foundation.Attached Files
Submitted - 1801.00749.pdf
Files
1801.00749.pdf
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Additional details
- Eprint ID
- 84074
- DOI
- 10.1007/s00454-017-9961-0
- Resolver ID
- CaltechAUTHORS:20180103-154009197
- N00014-11-1002
- Office of Naval Research (ONR)
- Gordon and Betty Moore Foundation
- Created
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2018-01-04Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field