Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/44192
Title: | Rational and real positive semidefinite rank can be different | Authors: | Fawzi, Hamza Gouveia, João Robinson, Richard Z. |
Issue Date: | 2016 | Publisher: | Elsevier | Project: | info:eu-repo/grantAgreement/FCT/5876/147205/PT | Serial title, monograph or event: | Operations Research Letters | Volume: | 44 | Issue: | 1 | Abstract: | Given a p×q nonnegative matrix M, the psd rank of MM is the smallest integer k such that there exist k×k real symmetric positive semidefinite matrices A_1,…,A_p and B_1,…,B_q such that M_ij=〈A_i,B_j〉for i=1,…,p and j=1,…,q. When the entries of M are rational it is natural to consider the rational-restricted psd rank of M, where the factors A_i and B_j are required to have rational entries. It is clear that the rational-restricted psd rank is always an upper bound to the usual psd rank. We show that this inequality may be strict by exhibiting a matrix with psd rank four whose rational-restricted psd rank is strictly greater than four. | URI: | https://hdl.handle.net/10316/44192 | DOI: | 10.1016/j.orl.2015.11.012 10.1016/j.orl.2015.11.012 |
Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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rational_psdrank.pdf | 296.1 kB | Adobe PDF | View/Open |
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