Exact solution for a matrix dynamical system with usual and Hadamard inverses

dc.creatorKorepanov, I. G.
dc.date2003-03-05
dc.date2003-03-13
dc.date.accessioned2026-07-07T05:34:35Z
dc.date.available2026-07-07T05:34:35Z
dc.descriptionLet 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.description10 pages; a few small improvements in this revised version
dc.identifierhttps://arxiv.org/abs/nlin/0303007
dc.identifierhttp://arxiv.org/abs/nlin/0303007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80420
dc.subjectExactly Solvable and Integrable Systems
dc.titleExact solution for a matrix dynamical system with usual and Hadamard inverses
dc.typetext

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