Four Deviations Suffice for Rank 1 Matrices

arXiv: Combinatorics, 2019.

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Abstract:

We prove a matrix discrepancy bound that strengthens the famous Kadison-Singer result of Marcus, Spielman, and Srivastava. Consider any independent scalar random variables $xi_1, ldots, xi_n$ with finite support, e.g. pm 1 }$ or ${ 0,1 }$-valued random variables, or some combination thereof. Let $u_1, dots, u_n mathbb{C}^m$ and $ sigma...More

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