Sums of Hermitian squares as an approach to the BMV conjecture


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BURGDORF, Sabine, 2011. Sums of Hermitian squares as an approach to the BMV conjecture. In: Linear and Multilinear Algebra. 59(1), pp. 1-9. ISSN 0308-1087. Available under: doi: 10.1080/03081080903119137

@article{Burgdorf2011Hermi-15309, title={Sums of Hermitian squares as an approach to the BMV conjecture}, year={2011}, doi={10.1080/03081080903119137}, number={1}, volume={59}, issn={0308-1087}, journal={Linear and Multilinear Algebra}, pages={1--9}, author={Burgdorf, Sabine} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dcterms:isPartOf rdf:resource=""/> <dc:date rdf:datatype="">2011-12-13T10:36:52Z</dc:date> <dcterms:title>Sums of Hermitian squares as an approach to the BMV conjecture</dcterms:title> <dc:creator>Burgdorf, Sabine</dc:creator> <bibo:uri rdf:resource=""/> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dspace:isPartOfCollection rdf:resource=""/> <dc:contributor>Burgdorf, Sabine</dc:contributor> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:language>eng</dc:language> <dcterms:issued>2011</dcterms:issued> <dcterms:abstract xml:lang="eng">Lieb and Seiringer stated in their reformulation of the Bessis-Moussa-Villani (BMV) conjecture that all coefficients of the polynomial p(t)=tr((A+tB)^m), where A and B are positive semidefinite matrices of the same size, are nonnegative. The coefficient of t^k is the trace of S_{m,k}(A, B), which is the sum of all words of length m in the letters A and B in which B appears exactly k times. We consider the case k=4 and show that S_{m,4}(A, B) is a sum of hermitian squares and commutators. In particular, the trace of S_{m,4}(A, B) is nonnegative.</dcterms:abstract> <dc:rights>terms-of-use</dc:rights> <dcterms:rights rdf:resource=""/> <dcterms:bibliographicCitation>Publ. in: Linear and Multilinear Algebra ; 59 (2011), 1. - pp. 1-9</dcterms:bibliographicCitation> <dcterms:available rdf:datatype="">2011-12-13T10:36:52Z</dcterms:available> </rdf:Description> </rdf:RDF>

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