An Inequality of Hadamard Type for Permanents
| dc.creator | Carlen, Eric | |
| dc.creator | Lieb, Elliott H. | |
| dc.creator | Loss, Michael | |
| dc.date | 2005-08-04 | |
| dc.date.accessioned | 2026-07-07T06:36:05Z | |
| dc.date.available | 2026-07-07T06:36:05Z | |
| dc.description | Let F be an N x N complex matrix whose jth column is the vector f_j in C^N. Let |f_j|^2 denote the sum of the absolute squares of the entries of f_j. Hadamard's inequality for determinants states that |\det(F)| <= \prod_{j=1}^N|f_j|. Here we prove a sharp upper bound on the permanent of F, which is |perm(F)| <= N!N^{-N/2} \prod_{j=1}^N|f_j|, and we determine all of the cases of equality. | |
| dc.description | 17 pages, latex | |
| dc.identifier | https://arxiv.org/abs/math/0508096 | |
| dc.identifier | http://arxiv.org/abs/math/0508096 | |
| dc.identifier | Methods and Applications of Analysis, vol 13, No. 1, pp 1-18 (March 2006) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99978 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 15A15; 26D20 | |
| dc.title | An Inequality of Hadamard Type for Permanents | |
| dc.type | text |