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arXiv · 1406.6326

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

Selden Crary
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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.

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Selden Crary. 2014-06-24. Factorization of the Determinant of the Gaussian-Correlation Matrix of Evenly Spaced Points Using an Inter-dimensional Multiset Duality. https://arxiv.org/abs/1406.6326

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