A comparison principle for functions of a uniformly random subspace

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.

8 pages

References in corpus (2)

• Multivariate normal approximation using exchangeable pairs
• How many entries of a typical orthogonal matrix can be approximated by independent normals?

Cited by in corpus (3)

• Quantum State Tomography for Matrix Product Density Operators
• Large deviation principles induced by the Stiefel manifold, and random multi-dimensional projections
• Low-rank matrix recovery via rank one tight frame measurements