Exact solution for a matrix dynamical system with usual and Hadamard inverses
| dc.creator | Korepanov, I. G. | |
| dc.date | 2003-03-05 | |
| dc.date | 2003-03-13 | |
| dc.date.accessioned | 2026-07-07T05:34:35Z | |
| dc.date.available | 2026-07-07T05:34:35Z | |
| dc.description | Let A be an n*n matrix with entries a_ij in the field C. Consider the following two involutive operations on such matrices: the matrix inversion I: A -> A^-1 and the element-by-element (or Hadamard) inversion J: a_ij -> a_ij^-1. We study the algebraic dynamical system generated by iterations of the product JI. In the case n=3, we give the full explicit solution for this system in terms of the initial matrix A. In the case n=4, we provide an explicit ansatz in terms of theta-functions which is full in the sense that it works for a Zariski open set of initial matrices. This ansatz also generalizes for higher n where it gives partial solutions. | |
| dc.description | 10 pages; a few small improvements in this revised version | |
| dc.identifier | https://arxiv.org/abs/nlin/0303007 | |
| dc.identifier | http://arxiv.org/abs/nlin/0303007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80420 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Exact solution for a matrix dynamical system with usual and Hadamard inverses | |
| dc.type | text |