A note on $l^2$ norms of weighted mean matrices

TL;DR

This paper provides a proof for Cartlidge's result concerning the $l^2$ operator norms of weighted mean matrices, interpreting these norms as eigenvalues of specific matrices.

Contribution

It offers a new proof of Cartlidge's result on $l^2$ norms, enhancing understanding of weighted mean matrices through eigenvalue interpretation.

Findings

Proof of Cartlidge's $l^2$ norm result

Interpretation of norms as eigenvalues of matrices

Clarification of weighted mean matrices' properties

Abstract

We give a proof of Cartlidge's result on the $l^{p}$ operator norms of weighted mean matrices for $p=2$ on interpreting the norms as eigenvalues of certain matrices.