Principal minor sums of (A+tB)m
Johnson, C. R., Leichenauer, S., MacNamara, P. R. W. and Costas, R. Linear Algebra and its Applications 411 (2005), 386 — 389Abstract
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},
}