The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach
Probability
2015-10-19 v2 Statistics Theory
Statistics Theory
Abstract
In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the random matrix and the expectation of the maximum squared norm achieved by one of the summands; there is also a weak dependence on the dimension of the random matrix. The purpose of this paper is to give a complete, elementary proof of this important, but underappreciated, inequality.
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Cite
@article{arxiv.1506.04711,
title = {The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach},
author = {Joel A. Tropp},
journal= {arXiv preprint arXiv:1506.04711},
year = {2015}
}
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20 pages