Improved bounds in Weaver's ${\mathrm{KS}}_r$ conjecture for high rank positive semidefinite matrices

Zhiqiang Xu, Zili Xu, Ziheng Zhu

Recently Marcus, Spielman and Srivastava proved Weaver's ${\mathrm{KS}}_r$ conjecture, which gives a positive solution to the Kadison-Singer problem. Cohen and Brändén independently ex…