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

@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:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/15309"> <dcterms:rights rdf:resource="http://nbn-resolving.org/urn:nbn:de:bsz:352-20140905103605204-4002607-1"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">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="http://kops.uni-konstanz.de/handle/123456789/15309"/> <dc:contributor>Burgdorf, Sabine</dc:contributor> <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>deposit-license</dc:rights> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-12-13T10:36:52Z</dcterms:available> <dcterms:bibliographicCitation>Publ. in: Linear and Multilinear Algebra ; 59 (2011), 1. - pp. 1-9</dcterms:bibliographicCitation> </rdf:Description> </rdf:RDF>

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