The LU-decomposition of Lehmer's tridiagonal matrix

TL;DR

This paper presents a method for deriving the LU-decomposition of Lehmer's tridiagonal matrix, enabling the calculation of its determinant through a rigorous proof of the initial guess.

Contribution

The paper introduces the first explicit LU-decomposition for Lehmer's tridiagonal matrix and provides a proof, facilitating determinant evaluation.

Findings

Explicit LU-decomposition derived and verified.

Determinant of Lehmer's matrix computed.

Method can be applied to similar matrices.

Abstract

The LU-decomposition of Lehmer's tridiagonal matrix is first guessed, then proved, which leads to an evaluation of the determinant.