Sums of Hermitian squares as an approach to the BMV conjecture

DOI10.1080/03081080903119137zbMath1229.13020arXiv0802.1153OpenAlexW2031729990WikidataQ122902174 ScholiaQ122902174MaRDI QIDQ3082847

Sabine Burgdorf

Publication date: 17 March 2011

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.1153

zbMATH Keywords

positive definite matrixtrace inequalityBessis-Moussa-Villani (BMV) conjecturewords in matrices

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Miscellaneous inequalities involving matrices (15A45) Quantum equilibrium statistical mechanics (general) (82B10) Real algebra (13J30)

Related Items (11)

Asymptotic positivity of Hurwitz product traces: two proofs ⋮ Conic Approach to Quantum Graph Parameters Using Linear Optimization Over the Completely Positive Semidefinite Cone ⋮ The BMV-conjecture over quaternions and octonions ⋮ A tracial Nullstellensatz ⋮ Proof of the BMV conjecture ⋮ The singular bivariate quartic tracial moment problem ⋮ The tracial moment problem on quadratic varieties ⋮ Sum-of-squares results for polynomials related to the Bessis-Moussa-Villani conjecture ⋮ Sums of squares over totally real fields are rational sums of squares ⋮ Sums of Hermitian squares and the BMV conjecture ⋮ A note on the nonexistence of sum of squares certificates for the Bessis–Moussa–Villani conjecture

Uses Software

• SeDuMi
• YALMIP
• NCAlgebra

Cites Work

• Advances on the Bessis-Moussa-Villani trace conjecture
• Equivalent forms of the Bessis-Moussa-Villani conjecture
• Sums of Hermitian squares and the BMV conjecture
• On the positivity of the coefficients of a certain polynomial defined by two positive definite matrices
• Connes' embedding conjecture and sums of Hermitian squares
• Proof of the cases \(p \leq 7\) of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture
• Monotonic converging variational approximations to the functional integrals in quantum statistical mechanics
• Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones

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