A note on the Gauss decomposition of the elliptic Cauchy matrix

TL;DR

This paper presents a straightforward derivation of explicit formulas for the Gauss decomposition of elliptic Cauchy matrices, leading to a direct proof of the elliptic Cauchy identity.

Contribution

It introduces a simple method to obtain the Gauss decomposition of elliptic Cauchy matrices, providing new explicit formulas and insights.

Findings

Explicit formulas for Gauss decomposition derived

Elliptic Cauchy identity obtained as a corollary

Simplified approach to elliptic Cauchy matrices

Abstract

Explicit formulas for the Gauss decomposition of elliptic Cauchy type matrices are derived in a very simple way. The elliptic Cauchy identity is an immediate corollary.