Factorization of the Determinant of the Gaussian-Correlation Matrix of Evenly Spaced Points Using an Inter-dimensional Multiset Duality
Statistics Theory
2019-05-29 v3 Statistics Theory
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.
Keywords
Cite
@article{arxiv.1406.6326,
title = {Factorization of the Determinant of the Gaussian-Correlation Matrix of Evenly Spaced Points Using an Inter-dimensional Multiset Duality},
author = {Selden Crary},
journal= {arXiv preprint arXiv:1406.6326},
year = {2019}
}
Comments
13 pages and 1 figure; Credit given to earlier proofs of Parts b and d of lemma