New determinantal representations of the W-weighted Drazin inverse over the quaternion skew field

TL;DR

This paper develops new determinantal formulas for the W-weighted Drazin inverse over quaternions, expanding the mathematical tools available for quaternion matrix analysis.

Contribution

It introduces novel determinantal representations of the W-weighted Drazin inverse using existing inverse representations and limit approaches.

Findings

New determinantal formulas for the W-weighted Drazin inverse

Representation of the inverse using existing inverse formulas

Application to quaternion matrix analysis

Abstract

Within the framework of the theory of the column and row determinants, we obtain new determinantal representations of the W-weighted Drazin inverse over the quaternion skew field. We give determinantal representations of the W-weighted Drazin inverse by using previously introduced determinantal representations of the Drazin inverse, the Moore-Penrose inverse, and the limit representations of the W-weighted Drazin inverse in some special case.