Paper: Principal minor sums of (A+tB)^m

Principal minor sums of (A+tB)^m

Abstract

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.

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BibTeX

@article {MR2178699,
AUTHOR={Johnson, C. R. and Leichenauer, S. and MacNamara, P. and Costas, R.},
TITLE={Principal minor sums of {$(A+tB)^m$}},
JOURNAL={Linear Algebra Appl.},
FJOURNAL={Linear Algebra and its Applications},
VOLUME={411},
YEAR={2005},
PAGES={386--389},
ISSN={0024-3795},
MRCLASS={15A15 (15A57)},
MRNUMBER={2178699},
ZBL={1086.15506},
MRREVIEWER={Peter M. Gibson},
DOI={10.1016/j.laa.2005.06.018},
URL={https://doi.org/10.1016/j.laa.2005.06.018},
}