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Published September 22, 2016 | public
Book Section - Chapter Open

The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach

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 inequality.

Additional Information

© 2016 Springer International Publishing Switzerland. First Online: 22 September 2016. The author wishes to thank Ryan Lee for a careful reading of the manuscript. The author gratefully acknowledges support from ONR award N00014-11-1002 and the Gordon & Betty Moore Foundation.

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