A comparison principle for functions of a uniformly random subspace

Details A comparison principle for functions of a uniformly random subspace A comparison principle for functions of a uniformly random subspace

2011-02-02

arxiv.org/abs/1102.0534v2

Mathematics

Probability

8 pages

Scientific paper

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.

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