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The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach

Tropp, Joel A. (2016) The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach. In: High Dimensional Probability VII. Progress in Probability (PRPR). No.71. Springer , Cham, pp. 173-202. ISBN 978-3-319-40517-9. http://resolver.caltech.edu/CaltechAUTHORS:20170214-075417526

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Abstract

In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the random matrix and the expectation of the maximum squared norm achieved by one of the summands; there is also a weak dependence on the dimension of the random matrix. The purpose of this paper is to give a complete, elementary proof of this important inequality.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/978-3-319-40519-3_8DOIArticle
http://link.springer.com/chapter/10.1007%2F978-3-319-40519-3_8PublisherArticle
https://arxiv.org/abs/1506.04711arXivDiscussion Paper
http://rdcu.be/ts9nPublisherFree ReadCube access
ORCID:
AuthorORCID
Tropp, Joel A.0000-0003-1024-1791
Additional Information:© 2016 Springer International Publishing Switzerland. First Online: 22 September 2016. The author wishes to thank Ryan Lee for a careful reading of the manuscript. The author gratefully acknowledges support from ONR award N00014-11-1002 and the Gordon & Betty Moore Foundation.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-11-1002
Gordon and Betty Moore FoundationUNSPECIFIED
Subject Keywords:Probability inequality; Random matrix; Sum of independent random variables
Classification Code:Mathematics Subject Classification (2010): 60B20; 60F10, 60G50, 60G42
Record Number:CaltechAUTHORS:20170214-075417526
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170214-075417526
Official Citation:Tropp J.A. (2016) The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach. In: Houdré C., Mason D., Reynaud-Bouret P., Rosiński J. (eds) High Dimensional Probability VII. Progress in Probability, vol 71. Birkhäuser, Cham
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74289
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Feb 2017 18:38
Last Modified:14 Jun 2017 20:47

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