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Sums of Hermitian squares as an approach to the BMV conjecture

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2011

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http://nbn-resolving.de/urn:nbn:de:bsz:352-153099
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https://doi.org/10.1080/03081080903119137
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Linear and Multilinear Algebra. 2011, 59(1), pp. 1-9. ISSN 0308-1087. Available under: doi: 10.1080/03081080903119137

Zusammenfassung

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.

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Fachgebiet (DDC)
510 Mathematik

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Bessis-Moussa-Villani (BMV) conjecture, sum of squares, trace inequality, semidefinite programming

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ISO 690BURGDORF, Sabine, 2011. Sums of Hermitian squares as an approach to the BMV conjecture. In: Linear and Multilinear Algebra. 2011, 59(1), pp. 1-9. ISSN 0308-1087. Available under: doi: 10.1080/03081080903119137
BibTex
@article{Burgdorf2011Hermi-15309,
  year={2011},
  doi={10.1080/03081080903119137},
  title={Sums of Hermitian squares as an approach to the BMV conjecture},
  number={1},
  volume={59},
  issn={0308-1087},
  journal={Linear and Multilinear Algebra},
  pages={1--9},
  author={Burgdorf, Sabine}
}
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