AI & Computingarticle2026-10-09

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

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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.

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View paper (DOI)Open access version OpenAlexAxiomsPublished 2026-10-09

Authors: Ziyang Pan, Zhiping Xiong, Yingying Qin

Institutions: Wuyi University, Wuyi University

Matrix Theory and Algorithms Holomorphic and Operator Theory Rings, Modules, and Algebras