Determinants and Limit Systems in some Idempotent and Non-Associative Algebraic Structure
Combinatorics
2020-10-09 v1
Abstract
This paper considers an idempotent and symmetrical algebraic structure as well as some closely related concept. A special notion of determinant is introduced and a Cramer formula is derived for a class of limit systems derived from the Hadamard matrix product and we give the algebraic form of a sequence of hyperplanes passing through a finite number of points. Thereby, some standard results arising for Max-Times systems with nonnegative entries appear as a special case. The case of two sided systems is also analyzed. In addition, a notion of eigenvalue in limit is considered. It is shown that one can construct a special semi-continuous regularized polynomial to find the eigenvalues of a matrix with nonnegative entries.
Cite
@article{arxiv.2010.04094,
title = {Determinants and Limit Systems in some Idempotent and Non-Associative Algebraic Structure},
author = {Walter Briec},
journal= {arXiv preprint arXiv:2010.04094},
year = {2020}
}