A lower bound for the Balan--Jiang matrix problem

Afonso S. Bandeira, Dustin G. Mixon, Stefan Steinerberger

We prove the existence of a positive semidefinite matrix $A\in {\mathbb{R}}^{n\times n}$ such that any decomposition into rank-1 matrices has to have factors with a large ${\ell }^1-$…