Positive semidefinite rank and nested spectrahedra

Kaie Kubjas, Elina Robeva, Richard Z. Robinson

Research output: Contribution to journalArticleScientificpeer-review

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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.
Original languageEnglish
Pages (from-to)1952-1974
JournalLINEAR AND MULTILINEAR ALGEBRA
Volume66
Issue number10
Early online date2017
DOIs
Publication statusPublished - 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • Mathematics - Algebraic Geometry
  • Mathematics - Optimization and Control
  • positive semidefinite rank
  • algebraic boundaries
  • spectrahedra
  • polytopes

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