On sufficient conditions for the total positivity and for the multiple positivity of matrices
| dc.creator | Katkova, Olga M. | |
| dc.creator | Vishnyakova, Anna M. | |
| dc.date | 2005-04-09 | |
| dc.date.accessioned | 2026-07-07T05:18:56Z | |
| dc.date.available | 2026-07-07T05:18:56Z | |
| dc.description | The following theorem is proved: Suppose $M = (a_{i,j})$ be a $k \times k$ matrix with positive entries and $a_{i,j}a_{i+1,j+1} > 4\cos ^2 \fracπ{k+1} a_{i,j+1}a_{i+1,j} \quad (1 \leq i \leq k-1, 1 \leq j \leq k-1).$ Then $\det M > 0 .$ The constant $4\cos ^2 \fracπ{k+1}$ in this Theorem is sharp. A few other results concerning totally positive and multiply positive matrices are obtained. Keywords: Multiply positive matrix; Totally positive matrix; Strictly totally positive matrix; Toeplitz matrix; Hankel matrix; Pólya frequency sequence. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0504183 | |
| dc.identifier | http://arxiv.org/abs/math/0504183 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74841 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 15A48; 15A57; 15A15 | |
| dc.title | On sufficient conditions for the total positivity and for the multiple positivity of matrices | |
| dc.type | text |