# Bounds on Spreads of Matrices related to Fourth Central Moment. II

## TL;DR

This paper establishes new inequalities involving the first four central moments of distributions, providing bounds for eigenvalues, matrix spreads, and polynomial roots, with a focus on real eigenvalues.

## Contribution

It introduces novel bounds on eigenvalues, matrix spreads, and polynomial roots based on fourth central moments, extending previous inequalities.

## Key findings

- Bounds for eigenvalues and matrix spread derived.
- Inequalities for roots and span of polynomials established.
- Applicable to matrices with real eigenvalues.

## Abstract

We derive some inequalities involving first four central moments of discrete and continuous distributions. Bounds for the eigenvalues and spread of a matrix are obtained when all its eigenvalues are real. Likewise, we discuss bounds for the roots and span of a polynomial equation.