Principal Minor Sums of (A+tB)m
Linear Algebra and its Applications
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.
McNamara, Peter; Johnson, Charles R.; Leichenauer, Stefan; and Costas, Roberto. "Principal Minor Sums of (A+tB)m." Linear Algebra and its Applications 411, (2005) : 386-389.