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2020 | 139 | 2 | 173-185
Article title

The Drazin inverse of a class of partitioned matrices

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EN
Abstracts
EN
In this work, we give the representations of the Drazin inverse for the partitioned matrix [■(A_1&A_2@O&A_3 )] with A_1 and A_3 square and singular under the conditions that rank(A_1 )=rank(A_3 )=1, Trace(A_1)≠0 and Trace(A_3)≠0, and then we give the representations of the Drazin inverse for the partitioned EP matrix [■(A_1&A_2@A_3&A_4 )] with A_1 is square and non-singular under the conditions that rank(A_1 )=rank([■(A_1&A_2@A_3&A_4 )]), and [■(A_1&A_2@A_3&A_4 )]=[■(I@P)] A_1 [■(I&Q)] where P=A_3 〖A_1〗^(-1) and Q= 〖A_1〗^(-1) A_2. Also, we give the representations of the Drazin inverse for the partitioned matrix [■(A_1&A_2@A_3&A_4 )] with A_1 square and singular under the conditions that rank(A_1 )=rank([■(A_1&A_2@A_3&A_4 )])=1, Trace([■(A_1&A_2@A_3&A_4 )])≠0.
Discipline
Year
Volume
139
Issue
2
Pages
173-185
Physical description
Contributors
  • Mathematics Department, Science Faculty, Sabratha University, Sabratha, Libya
References
  • [1] A. Ben-Israel, T. N. E. Greville, Generalized inverses: Theory and applications, Wiley, New York (1974).
  • [2] S. L. Campbell, C. D. Meyer, Jr., Generalized Inverses of Linear Transformations, Pitman, London, 1979.
  • [3] I. J. Katz, M. H. Pearl, On EPr and Normal EPr Matricas. Journal of Research of National Bureau of Standards - B. Mathematics and Mathematical Physics, 70B(1) (1966) 47-77.
  • [4] C. Bu, K. Zhang, The explicit representation of the Drazin inverse of a class of block matrices. Electron. J. Linear Algebra, 20 (2010) 406-418.
  • [5] C. Bu, K. Zhang, J. Zhao, Representation of the Drazin inverse on solution of a class singular differential equations. Linear and Multilinear Algebra, 59(8) (2011) 863-877.
  • [6] A. M. Kanan, K. Hassan, Solution of linear systems of differential equations with singular constant coefficients by the Drazin inverse of matrices. World Scientific News, 137 (2019) 229-236.
  • [7] Q. Xu., C. Song, X. Liu, General exact solutions of the second-order homogeneous algebraic differential equations. Linear and Multilinear Algebra, 36 (2015) 244-263.
Document Type
article
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-f5345b5c-3c8c-463d-b9a3-fd3573bb86a1
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