On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices
| dc.creator | Hillar, Christopher J. | |
| dc.creator | Johnson, Charles R. | |
| dc.date | 2007-07-05 | |
| dc.date.accessioned | 2026-07-07T08:14:05Z | |
| dc.date.available | 2026-07-07T08:14:05Z | |
| dc.description | It is shown that the polynomial \[p(t) = \text{Tr}[(A+tB)^m]\] has positive coefficients when $m = 6$ and $A$ and $B$ are any two 3-by-3 complex Hermitian positive definite matrices. This case is the first that is not covered by prior, general results. This problem arises from a conjecture raised by Bessis, Moussa and Villani in connection with a long-standing problem in theoretical physics. The full conjecture, as shown recently by Lieb and Seiringer, is equivalent to $p(t)$ having positive coefficients for any $m$ and any two $n$-by-$n$ positive definite matrices. We show that, generally, the question in the real case reduces to that of singular $A$ and $B$, and this is a key part of our proof. | |
| dc.description | 7 pages, J. Statistical Physics | |
| dc.identifier | https://arxiv.org/abs/0707.0712 | |
| dc.identifier | http://arxiv.org/abs/0707.0712 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132999 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Optimization and Control | |
| dc.title | On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices | |
| dc.type | text |