The question is raised whether the sum of the k-by-k principal minors of the titled matrix is a polynomial (in t) with positive coefficients, when A and B are positive-definite. This would generalize a conjecture made by Bessis-Moussa-Villani, as stated by Lieb and Seiringer. We give a variety of evidence for this further question, some of which is new.

The full atricle in pdf (Recommended), ps.