Hogben, L;
Palmowski, KF;
Roberson, DE;
Severini, S;
(2017)
Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions.
Electronic Journal of Linear Algebra
, 32
, Article 7. 10.13001/1081-3810.3102.
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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.
| Type: | Article |
|---|---|
| Title: | Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.13001/1081-3810.3102 |
| Publisher version: | http://dx.doi.org/10.13001/1081-3810.3102 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Projective rank, orthogonal representation, minimum positive semidefinite rank, fractional, Tsirelson’s problem, graph, matrix |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1530202 |
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