MP-weak Drazin matrices

doi:10.1080/03081087.2025.2588556

Return

MP-weak Drazin matrices

2025-11-01

PRE

Dijana Mosić

Milica Z. Kolundžija *

Mehdi Mohammadzadeh Karizaki

DOI：10.1080/03081087.2025.2588556

Original

Original request for help

Save

Abstract

En 中文

By employing the minimal rank weak Drazin inverse and the minimal rank right weak Drazin inverse, we study extended systems of matrix equations that generalize those whose solutions are $ A<^>\dag A<^>D $ A dagger AD and $ A<^>DA<^>\dag $ ADA dagger. We verify that new extended systems have solutions based on the Moore-Penrose inverse, minimal rank weak Drazin inverse and minimal rank right weak Drazin inverse of A, and these solutions are called Moore-Penrose weak Drazin and weak Drazin Moore-Penrose matrices, whose particular types are $ A<^>\dag A<^>D $ A dagger AD and $ A<^>DA<^>\dag $ ADA dagger. We investigate properties and characterizations of Moore-Penrose weak Drazin and weak Drazin Moore-Penrose matrices. As applications, we prove the solvability of some linear equations in terms of Moore-Penrose weak Drazin and weak Drazin Moore-Penrose matrices. Consequently, we get new characterizations of $ A<^>\dag A<^>D $ A dagger AD and $ A<^>DA<^>\dag $ ADA dagger as well as of new special cases of Moore-Penrose weak Drazin and weak Drazin Moore-Penrose matrices.

Keywords:

Minimal rank weak Drazin inverse

Drazin inverse

Moore-Penrose inverse