## 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 — 389

## 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}, }