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The Paulsen Problem Made Simple

Authors Linus Hamilton, Ankur Moitra

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  • Theory of computation → Design and analysis of algorithms
Keywords
  • radial isotropic position
  • operator scaling
  • Paulsen problem

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Abstract

The Paulsen problem is a basic problem in operator theory that was resolved in a recent tour-de-force work of Kwok, Lau, Lee and Ramachandran. In particular, they showed that every epsilon-nearly equal norm Parseval frame in d dimensions is within squared distance O(epsilon d^{13/2}) of an equal norm Parseval frame. We give a dramatically simpler proof based on the notion of radial isotropic position, and along the way show an improved bound of O(epsilon d^2).

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Linus Hamilton and Ankur Moitra. The Paulsen Problem Made Simple. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 41:1-41:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ITCS.2019.41

Author Details

Linus Hamilton
  • Massachusetts Institute of Technology, 77 Massachusetts Ave, USA
Ankur Moitra
  • Massachusetts Institute of Technology, 77 Massachusetts Ave, USA

Funding

  • Hamilton, Linus: This work was supported in part by a Fannie and John Hertz Foundation Fellowship.
  • Moitra, Ankur: This work was supported in part by NSF CAREER Award CCF-1453261, NSF Large CCF-1565235, a David and Lucile Packard Fellowship and an Alfred P. Sloan Fellowship.

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