  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
$O(\epsilon d^2)$.

Functional Analysis;Data Structures and Algorithms;Optimization and Control