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Published August 2012 | Published + Submitted
Journal Article Open

A comparison principle for functions of a uniformly random subspace

Tropp, Joel A.


This note demonstrates that it is possible to bound the expectation of an arbitrary norm of a random matrix drawn from the Stiefel manifold in terms of the expected norm of a standard Gaussian matrix with the same dimensions. A related comparison holds for any convex function of a random matrix drawn from the Stiefel manifold. For certain norms, a reversed inequality is also valid.

Additional Information

© 2011 The Author(s). This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. Received: 2 February 2011. Revised: 24 March 2011. Published online: 7 April 2011. The author would like to thank Ben Recht and Michael Todd for encouraging him to refine and present these results. Alex Gittens and Tiefeng Jiang provided useful comments on a preliminary draft of this article. The anonymous referees offered several valuable comments. This work has been supported in part by ONR awards N00014-08-1-0883 and N00014-11-1-0025, AFOSR award FA9550-09- 1-0643, and a Sloan Fellowship. Some of the research took place at Banff International Research Station (BIRS).

Attached Files

Submitted - 1102.0534.pdf

Published - Tropp2012p19176Probab_Theory_Rel.pdf


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August 19, 2023
August 19, 2023