A comparison principle for functions of a uniformly random subspace
Probability
2014-04-29 v2 Metric Geometry
Statistics Theory
Statistics Theory
Abstract
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.
Cite
@article{arxiv.1102.0534,
title = {A comparison principle for functions of a uniformly random subspace},
author = {Joel A. Tropp},
journal= {arXiv preprint arXiv:1102.0534},
year = {2014}
}
Comments
8 pages