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The Infinite Lights out Problem and Symmetric Matrices over Z2.

Daniel Goncalves1, Cardoso Gongalves*1
1Departamento de Matematica – Universidade Federal de Santa Catarina Trindade – Floriandépolis – SC – 88.040-900 – Brazil.

Abstract

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

Keywords: Infinite matrices, lights out, symmetric matrices, diagonal, range