Remarks on some majorization inequalities

TL;DR

This paper revisits and extends majorization inequalities related to eigenvalues, focusing on Hiroshima's theorem, providing new insights, discussions, and open problems in the field.

Contribution

It extends Hiroshima's eigenvalue majorization theorem and offers new perspectives and open questions in the study of eigenvalue inequalities.

Findings

Extended Hiroshima's majorization theorem.

Provided new inequalities and bounds.

Discussed open problems in eigenvalue majorization.

Abstract

This note revisits some majorization inequalities for eigenvalues, special attention is given to an elegant theorem of Hiroshima. An extension of the special case of Hiroshima's theorem is presented. Some discussion and open problems are also included.