Factorization of the Determinant of the Gaussian-Correlation Matrix of Evenly Spaced Points Using an Inter-dimensional Multiset Duality

Abstract

We prove that the determinant of a Gaussian-correlation matrix V of n evenly spaced points has leading power n(n-1) in the nearest-neighbor distance between points. The proof uses Neville elimination to determine all elements of the upper triangular matrix U of V and provides a factorization of det(V). The proof makes use of an inter-dimensional multiset duality involving simplices that emerge during the factorization. We conjecture that V for evenly spaced points is strictly totally positive.