A comparison principle for functions of a uniformly random subspace
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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.
8 pages
- California Institute of Technology United States
Statistics and Probability, 60B20, Probability (math.PR), Mathematics - Statistics Theory, Metric Geometry (math.MG), Statistics Theory (math.ST), 004, Mathematics - Metric Geometry, FOS: Mathematics, Statistics, Probability and Uncertainty, Analysis, Mathematics - Probability
Statistics and Probability, 60B20, Probability (math.PR), Mathematics - Statistics Theory, Metric Geometry (math.MG), Statistics Theory (math.ST), 004, Mathematics - Metric Geometry, FOS: Mathematics, Statistics, Probability and Uncertainty, Analysis, Mathematics - Probability
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