Positive semidefinite rank and nested spectrahedra

Kaie Kubjas; Elina Robeva; Richard Z. Robinson

doi:10.1080/03081087.2017.1381664

Positive semidefinite rank and nested spectrahedra

Kaie Kubjas, Elina Robeva, Richard Z. Robinson

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

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Abstrakti

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.

Alkuperäiskieli	Englanti
Sivut	1952-1974
Julkaisu	Linear and Multilinear Algebra
Vuosikerta	66
Numero	10
Varhainen verkossa julkaisun päivämäärä	2017
DOI - pysyväislinkit	https://doi.org/10.1080/03081087.2017.1381664
Tila	Julkaistu - 2018
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Pääsy asiakirjaan

10.1080/03081087.2017.1381664

PostprintAccepted author manuscript, 2,5 MB

http://adsabs.harvard.edu/abs/2015arXiv151208766K

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title = "Positive semidefinite rank and nested spectrahedra",

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 = "Mathematics - Algebraic Geometry, Mathematics - Optimization and Control, positive semidefinite rank, algebraic boundaries, spectrahedra, polytopes",

author = "Kaie Kubjas and Elina Robeva and Robinson, {Richard Z.}",

year = "2018",

doi = "10.1080/03081087.2017.1381664",

language = "English",

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pages = "1952--1974",

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T1 - Positive semidefinite rank and nested spectrahedra

AU - Kubjas, Kaie

AU - Robeva, Elina

AU - Robinson, Richard Z.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Mathematics - Algebraic Geometry

KW - Mathematics - Optimization and Control

KW - positive semidefinite rank

KW - algebraic boundaries

KW - spectrahedra

KW - polytopes

U2 - 10.1080/03081087.2017.1381664

DO - 10.1080/03081087.2017.1381664

M3 - Article

SN - 0308-1087

VL - 66

SP - 1952

EP - 1974

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 10

ER -

Positive semidefinite rank and nested spectrahedra

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