English

Infinite Symmetric Matrices over Z_2 and the Lights Out Problem

Combinatorics 2013-06-24 v1 Rings and Algebras

Abstract

We show, using a hybrid analysis/linear algebra argument, that the diagonal vector of an infinite symmetric matrix over Z2{\mathbb Z}_2 is contained in the range of the matrix. We apply this result to an extension, to the countable infinite case, of the Lights Out problem.

Keywords

Cite

@article{arxiv.1306.5007,
  title  = {Infinite Symmetric Matrices over Z_2 and the Lights Out Problem},
  author = {Daniel Gonçalves and Maria Inez Cardoso Gonçalves},
  journal= {arXiv preprint arXiv:1306.5007},
  year   = {2013}
}