A Note on the Drazin Inverse of 2 × 2 Block Triangular Matrices

By using the forward order law for the Drazin inverse of matrix products, we investigate the Drazin inverse of 2×2 block triangular matrices. A necessary and sufficient condition for ABOCD=ADBDOCD is presented. Notably, this condition is expressed exclusively in terms of rank equalities.

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Publication Details

Journal
Axioms
Published
2026-10-09
DOI
https://doi.org/10.3390/axioms15100750
Primary Topic
Matrix Theory and Algorithms
Type
article
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article

A Note on the Drazin Inverse of 2 × 2 Block Triangular Matrices

Zhiping Xiong, Yingying Qin, Ziyang Pan
Axioms
Matrix Theory and Algorithms
article

A Note on the Drazin Inverse of 2 × 2 Block Triangular Matrices

Zhiping Xiong, Yingying Qin, Ziyang Pan
article en

Abstract

By using the forward order law for the Drazin inverse of matrix products, we investigate the Drazin inverse of 2×2 block triangular matrices. A necessary and sufficient condition for ABOCD=ADBDOCD is presented. Notably, this condition is expressed exclusively in terms of rank equalities.

AxiomsVol. 15(10)
Wuyi University (CN), Wuyi University (CN)
Openalex Percentile: Top 14%
Matrix Theory and Algorithms
DOIOpen Access PDFOpenAlex
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A Note on the Drazin Inverse of 2 × 2 Block Triangular Matrices — Zhiping Xiong, Yingying Qin, et al. · Axioms (2026) | TGRS Research Map | TGRS