Symbolic estimation of distances between eigenvalues of Hermitian operator

TL;DR

This paper introduces a symbolic method using Hankel matrices to estimate the minimal and maximal distances between eigenvalues of Hermitian matrices and roots of real polynomials, including their range of locations, with arbitrary precision.

Contribution

It presents a novel symbolic approach for estimating eigenvalue distances and locations of Hermitian matrices and real polynomials using Hankel matrix formalism.

Findings

Effective symbolic estimation of eigenvalue distances

Range of eigenvalue locations can be symbolically determined

Estimations are precise to any desired level

Abstract

We find out a method for symbolic estimation of a minimal (maximal) distance between eigenvalues of a Hermitian matrix (or roots of a polynomial with real (maybe degenerated) roots), using Hankel matrices formalism. The range of location of eigenvalues is symbolically estimated too. All estimations can be done with any precision.