Skip to content
DraconiticResearch
Search Sources API
197,761 studies31 sourcesUpdated 3 min ago
Peer-reviewedCC BY 4.0Axioms

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

  • Ziyang Pan1
  • Zhiping Xiong1
  • Yingying Qin1
  1. 1School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China
Open at sourceDOICite

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.

Related

  1. Laws for triangular matrices
    Xun Hu, Yanfeng Luo, Mikhail Volkov
    arXivPreprintarXiv licenceFull textAlgebra & number theoryLogic & foundationsarXiv
  2. The Karcher Mean on Lie Groups of Upper Triangular Matrices
    Huajun Huang, Jimmie Lawson
    arXivPreprintCC BY-NC-SA 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv
  3. Randomized inexact block triangular preconditioners for double saddle-point systems in PDE-constrained optimization
    Siqi Liang, Na Huang
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. D(N)-quadruples in upper-triangular 2×2 integer matrices
    Andrej Dujella, Zrinka Franušić
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. The Karcher Mean on 2× 2 Triangular Matrices with Positive Diagonal Entries
    Huajun Huang
    arXivPreprintCC BY-NC-SA 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@article{pan2026note,
  title = {{A Note on the Drazin Inverse of 2 × 2 Block Triangular Matrices}},
  author = {Ziyang Pan and Zhiping Xiong and Yingying Qin},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100750},
  url = {https://www.mdpi.com/2075-1680/15/10/750},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Note on the Drazin Inverse of 2 × 2 Block Triangular Matrices
AU  - Ziyang Pan
AU  - Zhiping Xiong
AU  - Yingying Qin
PY  - 2026
DA  - 2026/10/09
JO  - Axioms
DO  - 10.3390/axioms15100750
UR  - https://www.mdpi.com/2075-1680/15/10/750
AB  - 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.
SN  - 2075-1680
ER  -