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Indian Journal of Pure and Applied Mathematics

, Volume 50, Issue 4, pp 837–847 | Cite as

Core invertibility of triangular matrices over a ring

  • Sanzhang XuEmail author
Article
  • 22 Downloads

Abstract

We obtained several equivalent conditions for the existence of core inverses and dual core inverses of triangular matrices over a ring with involution. As applications, some necessary and sufficient conditions for the (2,2,0) core inverse problem are given.

Key words

Core inverse dual core inverse group inverse ring triangular matrix 

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Notes

Acknowledgement

The author is grateful to China Scholarship Council for giving him a purse for his further study in Universidad Politécnica de Valencia, Spain. Research is supported by the Natural Science Foundation of Jiangsu Education Committee (No. 19KJB110005) and the Natural Science Foundation of Jiangsu Province of China (No. BK20191047).

References

  1. 1.
    O. M. Baksalary and G. Trenkler, Core inverse of matrices, Linear Multilinear Algebra, 58(6) (2010), 681–697.MathSciNetCrossRefGoogle Scholar
  2. 2.
    R. E. Hartwig and K. Spindelböck, Matrices for which A* and A commmute, Linear Multilinear Algebra, 14 (1984), 241–256.CrossRefGoogle Scholar
  3. 3.
    R. E. Hartwig and J. Shoaf, Group inverses and Drazin inverses of bidiagonal and triangular toeplitz matrices, J. Austral. Math. Soc., 24 (1977), 10–34.MathSciNetCrossRefGoogle Scholar
  4. 4.
    P. Puystjens and R. E. Hartwig, The group inverse of a companion matrix, Linear Multilinear Algebra, 43 (1997), 137–150.MathSciNetCrossRefGoogle Scholar
  5. 5.
    D. S. Rakić, Nebojša Č. Dinčić, and D. S. Djordjević, Group, Moore-Penrose, core and dual core inverse in rings with involution, Linear Algebra Appl., 463 (2014), 115–133.MathSciNetCrossRefGoogle Scholar
  6. 6.
    H. X. Wang, Core-EP decomposition and its applications, Linear Algebra Appl., 508 (2016), 289–300.MathSciNetCrossRefGoogle Scholar
  7. 7.
    H. X. Wang and X. J. Liu, Characterizations of the core inverse and the partial ordering, Linear Multilinear Algebra, 63(9) (2015), 1829–1836.MathSciNetCrossRefGoogle Scholar
  8. 8.
    S. Z. Xu, J. L. Chen, and X. X. Zhang, New characterizations for core and dual core inverses in rings with involution, Front. Math. China, 12(1) (2017), 231–246.MathSciNetCrossRefGoogle Scholar

Copyright information

© Indian National Science Academy 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsHuaiyin Institute of TechnologyHuaianP. R. China

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