Positive semidefinite rank and nested spectrahedra

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Author
Date
2018
Department
Statistics and Mathematical Data Science
Massachusetts Institute of Technology MIT
University of Washington
Department of Mathematics and Systems Analysis
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Mcode
Degree programme
Language
en
Pages
1952-1974
Series
LINEAR AND MULTILINEAR ALGEBRA, Volume 66, issue 10
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.
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Keywords
Mathematics - Algebraic Geometry, Mathematics - Optimization and Control, positive semidefinite rank, algebraic boundaries, spectrahedra, polytopes
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DOI
10.1080/03081087.2017.1381664
Citation
Kubjas , K , Robeva , E & Robinson , R Z 2018 , ' Positive semidefinite rank and nested spectrahedra ' , LINEAR AND MULTILINEAR ALGEBRA , vol. 66 , no. 10 , pp. 1952-1974 . https://doi.org/10.1080/03081087.2017.1381664
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https://urn.fi/URN:NBN:fi:aalto-202001021093
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[article-cris] Perustieteiden korkeakoulu / SCI