Principal Minor Sums of (A+tB)m

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Linear Algebra and its Applications, Page: 386-389

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McNamara, Peter; Johnson, Charles R.; Leichenauer, Stefan; Costas, Roberto
article description
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.