Note on the spread of real symmetric matrices with entries in fixed interval

TL;DR

This paper investigates the maximum eigenvalue spread of real symmetric matrices with entries in a fixed interval, providing theoretical insights and extending previous results to understand how entry restrictions influence eigenvalue distribution.

Contribution

It offers new theoretical results on spread maximization for symmetric matrices with interval-restricted entries, building upon prior work by Zhan, Fallat, and Xing.

Findings

Derived bounds for eigenvalue spread in interval-restricted matrices

Extended existing results to broader classes of symmetric matrices

Provided conditions for spread maximization in constrained matrix sets

Abstract

The spread of a matrix is defined as the maximum of distances between any two eigenvalues of that matrix. In this paper we investigate spread maximization as a function on compact convex subset of the set of real symmetric matrices. We provide some general results and further, we study spread maximizing problem on the set of symmetric matrices with entries restricted to the interval. In particular, we develop some results by X. Zhan, S. M. Fallat and J. J. Xing.