Global properties of eigenvalues of parametric rank one perturbations for unstructured and structured matrices II

TL;DR

This paper corrects and refines previous results on the eigenvalues of parametric rank one perturbations for both structured and unstructured matrices, enhancing the accuracy of eigenvalue estimates.

Contribution

It provides a correction to a key theorem and improves the eigenvalue estimates for rank one perturbations in structured and unstructured matrices.

Findings

Corrected Theorem 17 from earlier work

Sharpened eigenvalue estimates for rank one perturbations

Enhanced understanding of eigenvalue behavior in matrix perturbations

Abstract

We present in this note a correction to Theorem 17 in our earlier paper "Global properties of eigenvalues of parametric rank one perturbations for structured and unstructured matrices" and sharpen the estimates for eigenvalues of parametric rank one perturbations given in that theorem.