Corpus ID: 235458432

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

  title={Improved bounds in Weaver's \$\{\rm KS\}\_r\$ conjecture for high rank positive semidefinite matrices},
  author={Zhiqiang Xu and Zili Xu and Ziheng Zhu},
Recently Marcus, Spielman and Srivastava proved Weaver’s KSr conjecture, which gives a positive solution to the Kadison-Singer problem. In [Coh16, Brä18], Cohen and Brändén independently extended this result to obtain the arbitrary-rank version of Weaver’s KSr conjecture. In this paper, we present a new bound in Weaver’s KSr conjecture for the arbitrary-rank case. To do that, we introduce the definition of (k,m)characteristic polynomials and employ it to improve the previous estimate on the… Expand

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