Eigenvector sensitivity under general and structured perturbations of tridiagonal Toeplitz-type matrices

TL;DR

This paper investigates how eigenvectors of tridiagonal Toeplitz-type matrices respond to various perturbations, filling a gap in understanding eigenvector sensitivity beyond eigenvalues.

Contribution

It provides new analysis of eigenvector sensitivity for structured matrices under general and structured perturbations, an area less explored in prior research.

Findings

Eigenvector sensitivity varies with perturbation type and matrix structure.

Error bounds for eigenvector perturbations are established.

Insights into pseudospectrum behavior for Toeplitz-type matrices.

Abstract

The sensitivity of eigenvalues of structured matrices under general or structured perturbations of the matrix entries has been thoroughly studied in the literature. Error bounds are available and the pseudospectrum can be computed to gain insight. Few investigations have focused on analyzing the sensitivity of eigenvectors under general or structured perturbations. The present paper discusses this sensitivity for tridiagonal Toeplitz and Toeplitz-type matrices.