Advances on the Bessis-Moussa-Villani trace conjecture

DOI10.1016/j.laa.2007.04.005zbMath1126.15024arXivmath/0507166OpenAlexW2065269914WikidataQ123018432 ScholiaQ123018432MaRDI QIDQ996225

Christopher J. Hillar

Publication date: 13 September 2007

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

Full work available at URL: https://arxiv.org/abs/math/0507166

zbMATH Keywords

Euler-Lagrange equationpositive definite matrixtrace inequalityBessis-Moussa-Villani (BMV) conjecturewords in two matrices

Mathematics Subject Classification ID

Variational inequalities (49J40) Determinants, permanents, traces, other special matrix functions (15A15) Miscellaneous inequalities involving matrices (15A45)

Related Items

On D. Hägele's approach to the Bessis-Moussa-Villani conjecture ⋮ Asymptotic positivity of Hurwitz product traces: two proofs ⋮ The BMV-conjecture over quaternions and octonions ⋮ Proof of the cases \(p \leq 7\) of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture ⋮ Proof of the BMV conjecture ⋮ 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 new series of conjectures and open questions in optimization and matrix analysis ⋮ Sums of Hermitian squares as an approach to the BMV conjecture ⋮ NCSOStools: a computer algebra system for symbolic and numerical computation with noncommutative polynomials ⋮ A note on the nonexistence of sum of squares certificates for the Bessis–Moussa–Villani conjecture

Cites Work

• Unnamed Item
• Equivalent forms of the Bessis-Moussa-Villani conjecture
• On the positivity of the coefficients of a certain polynomial defined by two positive definite matrices
• A hyper-geometric approach to the BMV-conjecture
• 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
• Eigenvalues of Words in Two Positive Definite Letters
• Trace functions as Laplace transforms
• Matrix Analysis
• Representation of the function Tr(exp(A - λB)) as a Laplace transform with positive weight and some matrix inequalities
• ON THE REPRESENTATION OF Tr(e^(A-λB)) AS A LAPLACE TRANSFORM
• Perturbation of Wigner matrices and a conjecture