English

Positive semidefinite rank and nested spectrahedra

Algebraic Geometry 2017-01-11 v2 Optimization and Control

Abstract

The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general values of positive semidefinite rank we provide a conjecture for the description of this boundary. Our proof techniques are geometric in nature and rely on nesting spectrahedra between polytopes.

Keywords

Cite

@article{arxiv.1512.08766,
  title  = {Positive semidefinite rank and nested spectrahedra},
  author = {Kaie Kubjas and Elina Robeva and Richard Z. Robinson},
  journal= {arXiv preprint arXiv:1512.08766},
  year   = {2017}
}

Comments

23 pages

R2 v1 2026-06-22T12:19:39.853Z