Infinite Symmetric Matrices over Z_2 and the Lights Out Problem

Abstract

We show, using a hybrid analysis/linear algebra argument, that the diagonal vector of an infinite symmetric matrix over ${\mathbb{Z}}_2$ 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.

References in corpus (1)

• Symmetric Matrices over F_2 and the Lights Out Problem