Note on eigenvectors from eigenvalues

TL;DR

This paper extends a method for deriving eigenvectors from eigenvalues, originally applicable to Hermitian matrices with distinct eigenvalues, to include all Hermitian matrices, broadening its applicability.

Contribution

It generalizes a previous eigenvector derivation method to encompass all Hermitian matrices, not just those with distinct eigenvalues.

Findings

Method now applies to all Hermitian matrices

Maintains accuracy in eigenvector determination

Broadens applicability of eigenvector extraction techniques

Abstract

Denton, Parke, Tao and Zhang gave a new method which determines eigenvectors from eigenvalues for Hermitian matrices with distinct eigenvalues. In this short note, we extend the above result to general Hermitian matrices.