Inverse tridiagonal Z-matrices
| dc.creator | McDonald, J. J. | |
| dc.creator | Nabben, R. | |
| dc.creator | Neumann, M. | |
| dc.creator | Schneider, H. | |
| dc.creator | Tsatsomeros, M. | |
| dc.date | 1998-03-25 | |
| dc.date.accessioned | 2026-07-07T05:24:12Z | |
| dc.date.available | 2026-07-07T05:24:12Z | |
| dc.description | In this paper, we consider matrices whose inverses are tridiagonal Z--matrices. Based on a characterization of symmetric tridiagonal matrices by Gantmacher and Krein, we show that a matrix is the inverse of a tridiagonal Z--matrix if and only if, up to a positive scaling of the rows, it is the Hadamard product of a so called weak type $\D$ matrix and a flipped weak type $\D$ matrix whose parameters satisfy certain quadratic conditions. We predict from these parameters to which class of Z--matrices the inverse belongs to. In particular, we give a characterization of inverse tridiagonal M--matrices. Moreover, we characterize inverses of tridiagonal M--matrices that satisfy certain row sum criteria. This leads to the cyclopses that are matrices constructed from type $\D$ and flipped type $\D$ matrices. We establish some properties of the cyclopses and provide explicit formulae for the entries of the inverse of a nonsingular cyclops. We also show that the cyclopses are the only generalized ultrametric matrices whose inverses are tridiagonal. | |
| dc.identifier | https://arxiv.org/abs/math/9803125 | |
| dc.identifier | http://arxiv.org/abs/math/9803125 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76746 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Combinatorics | |
| dc.subject | 15A48, 05-XX | |
| dc.title | Inverse tridiagonal Z-matrices | |
| dc.type | text |