Generalized Inverse Preservers of Hadamard Circulant Majorization

TL;DR

This paper investigates how certain matrix inverses preserve a specific majorization property related to Hadamard circulant matrices, extending known results to generalized inverses.

Contribution

It demonstrates that the Moore-Penrose, group, and Drazin inverses inherit the Hadamard circulant majorization preservation property.

Findings

Moore-Penrose inverse preserves Hadamard circulant majorization.

Group inverse preserves Hadamard circulant majorization.

Drazin inverse preserves Hadamard circulant majorization.

Abstract

Let $T\colon M_n\rightarrow M_n$ preserve Hadamard circulant majorization. In this note, we show that this property is inherited by the three most popular generalized inverses, viz. the Moore-Penrose inverse, the group inverse and the Drazin inverse.