On Generalized Weighted Hilbert Matrices

TL;DR

This paper investigates the spectral properties of generalized weighted Hilbert matrices, including their spectral norm, determinant, eigenvalues, and eigenvectors, and examines the asymptotic behavior of the classical Hilbert matrix's spectral norm.

Contribution

It provides new theoretical results on the spectral characteristics of generalized weighted Hilbert matrices and their asymptotic properties.

Findings

Spectral norm and determinant formulas derived

Relations between eigenvalues and eigenvectors established

Asymptotic behavior of classical Hilbert matrix spectral norm analyzed

Abstract

In this paper, we study spectral properties of generalized weighted Hilbert matrices. In particular, we establish results on the spectral norm, determinant, as well as various relations between the eigenvalues and eigenvectors of such matrices. We also study the asymptotic behaviour of the spectral norm of the classical Hilbert matrix.