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 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}
}