# Gradient of eigenvalues of Dirac operators and its applications

## TL;DR

This paper introduces a method to compute the gradients of eigenvalues of Dirac operators using normalized eigenfunctions, and explores their applications in describing isospectral operators and spectral data modifications.

## Contribution

It provides explicit formulas for eigenvalue gradients of Dirac operators and demonstrates their use in spectral analysis and operator characterization.

## Key findings

- Derived formulas for eigenvalue gradients in terms of eigenfunctions
- Applied gradients to identify isospectral operators
- Analyzed effects of changing finite spectral data

## Abstract

For Dirac operators, which have discrete spectra, the concept of eigenvalues gradient is given and formulae for this gradients are obtained in terms of normalized eigenfunctions. It is shown how the gradient is being used to describe isospectral operators or when finite number of spectral data is changed.