TY - JOUR T1 - Principal minor sums of (A+tB)m AU - Johnson, Charles R. AU - Leichenauer, Stefan AU - McNamara, Peter AU - Costas, Roberto JO - Linear Algebra and its Applications VL - 411 SP - 386 EP - 389 PY - 2005 DA - 2005/12/01/ T2 - Special Issue on Determinants and the Legacy of Sir Thomas Muir SN - 0024-3795 DO - https://doi.org/10.1016/j.laa.2005.06.018 UR - https://www.sciencedirect.com/science/article/pii/S0024379505003137 KW - Positive definite matrix KW - Principal minors AB - The question is raised whether the sum of the k×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 E.H. Lieb and R. Seiringer [Equivalent forms of the Bessis–Moussa–Villani conjecture, J. Stat. Phys. 115 (2004) 185–190]. We give a variety of evidence for this further question, some of which is new. ER -