Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

4-2017

Journal or Book Title

Electronic Journal of Linear Algebra

Volume

32

First Page

98

Last Page

115

DOI

10.13001/1081-3810.3102

Abstract

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.

Comments

This article is published as Hogben, Leslie, Kevin Palmowski, David Roberson, and Simone Severini. "Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions." The Electronic Journal of Linear Algebra 32 (2017): 98-115. DOI: 10.13001/1081-3810.3102. Posted with permission.

Copyright Owner

The Author(s)

Language

en

File Format

application/pdf

Included in

Algebra Commons

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