Eigenfunction properties and approximations of selected incidence matrices employed in spatial analyses Original Research Article

Mathematical properties of eigenfunctions of selected incidence matrices appearing in spatial statistics formulae are summarized. Seven theorems are proposed and proved, and three conjectures are posited. Results summarized here allow the determinant of massively large n×n geographic weights matrices to be accurately approximated. In addition, the behavior of eigenfunctions for graphs affiliated with a linear configuration of connected nodes are better understood.