Work

A Note on Representations of the Drazin Inverse for Complex Partitioned Matrices

Year: 2026

Type: article

Abstract: In this paper, we present explicit representations for Drazin inverses of the sum P+Q under the conditions P2Q=0, Q2PQ=0, and Q(PQ)2=0. Then, we apply our results to derive a series of representations for the Drazin inverses of a 2×2 complex partitioned matrix ABCD, where A and D are square complex matrices. Numerical examples are provided to show that the assumptions used here are genuinely weaker than those in a number of earlier results.

Source: Mathematics

DOI: 10.3390/math14111856

Authors: Yue Zhao, Daochang Zhang, Dijana Mosić

Institutions: Georgia State University, Northeast Electric Power University, University of Nis

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation