Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions

Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions

Fractional minimum positive semidefinite rank is defined from r-fold faithful orthogonal representations and it is shown that the projective rank of any graph equals the fractional minimum positive semidefinite rank of its complement. An r-fold version of the traditional definition of minimum positi...

Full description

Saved in:
Bibliographic Details
Main Authors: Hogben, Leslie, Palmowski, Kevin F, Roberson, David E, Severini, Simone
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2017
Subjects:
Orthogonal representation
Projective rank
Online Access:https://hdl.handle.net/10356/83454
http://hdl.handle.net/10220/43551
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-83454
record_format dspace
spelling sg-ntu-dr.10356-834542023-02-28T19:33:42Z Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions Hogben, Leslie Palmowski, Kevin F Roberson, David E Severini, Simone School of Physical and Mathematical Sciences Orthogonal representation Projective rank Fractional minimum positive semidefinite rank is defined from r-fold faithful orthogonal representations and it is shown that the projective rank of any graph equals the fractional minimum positive semidefinite rank of its complement. An r-fold version of the traditional definition of minimum positive semidefinite rank of a graph using Hermitian matrices that fit the graph is also presented. This paper also introduces r-fold orthogonal representations of graphs and formalizes the understanding of projective rank as fractional orthogonal rank. Connections of these concepts to quantum theory, including Tsirelson's problem, are discussed. NRF (Natl Research Foundation, S’pore) Published version 2017-08-04T06:25:14Z 2019-12-06T15:23:19Z 2017-08-04T06:25:14Z 2019-12-06T15:23:19Z 2017 Journal Article Hogben, L., Palmowski, K. F., Roberson, D. E., & Severini, S. (2017). Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions. Electronic Journal of Linear Algebra, 32, 98-115. 1081-3810 https://hdl.handle.net/10356/83454 http://hdl.handle.net/10220/43551 10.13001/1081-3810.3102 en Electronic Journal of Linear Algebra © 2017 The Author(s) (Published by International Linear Algebra Society). This paper was published in Electronic Journal of Linear Algebra and is made available as an electronic reprint (preprint) with permission of The Author(s) (Published by International Linear Algebra Society). The published version is available at: [http://dx.doi.org/10.13001/1081-3810.3102]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. 18 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Orthogonal representation
Projective rank
spellingShingle Orthogonal representation
Projective rank
Hogben, Leslie
Palmowski, Kevin F
Roberson, David E
Severini, Simone
Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions
description Fractional minimum positive semidefinite rank is defined from r-fold faithful orthogonal representations and it is shown that the projective rank of any graph equals the fractional minimum positive semidefinite rank of its complement. An r-fold version of the traditional definition of minimum positive semidefinite rank of a graph using Hermitian matrices that fit the graph is also presented. This paper also introduces r-fold orthogonal representations of graphs and formalizes the understanding of projective rank as fractional orthogonal rank. Connections of these concepts to quantum theory, including Tsirelson's problem, are discussed.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Hogben, Leslie
Palmowski, Kevin F
Roberson, David E
Severini, Simone
format Article
author Hogben, Leslie
Palmowski, Kevin F
Roberson, David E
Severini, Simone
author_sort Hogben, Leslie
title Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions
title_short Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions
title_full Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions
title_fullStr Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions
title_full_unstemmed Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions
title_sort orthogonal representations, projective rank, and fractional minimum positive semidefinite rank: connections and new directions
publishDate 2017
url https://hdl.handle.net/10356/83454
http://hdl.handle.net/10220/43551
_version_ 1759855710979489792

Similar Items