Open AccessOn the Drazin inverse of anti-triangular block matrices
Author(s) -
Daochang Zhang,
Dijana Mosić,
Liangyun Chen
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022124
Subject(s) - drazin inverse , mathematics , triangular matrix , block (permutation group theory) , inverse , block matrix , matrix (chemical analysis) , pure mathematics , complex matrix , algebra over a field , combinatorics , invertible matrix , eigenvalues and eigenvectors , geometry , chemistry , physics , chromatography , quantum mechanics
Our aim is to present new expressions for the Drazin inverse of anti-triangular block matrices under some circumstances. Applying the established new formulae for anti-triangular block matrices, we derive explicit representations for the Drazin inverse of a $ 2\times2 $ complex block matrix under corresponding assumptions. We extend several well known results in the literature in this way.