2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170552It is shown that the polynomial $λ(t) = {\rm Tr}[(A + tB)^p]$ has nonnegative coefficients when $p \leq 7$ and A and B are any two complex positive semidefinite $n \times n$ matrices with arbitrary $n$. This proofs a general nontrivial case of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture which is a long standing problem in theoretical physics.5 pages; typos corrected; accepted for publication in Journal of Statistical PhysicsFunctional AnalysisOperator Algebrastext