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Number of results
2019 | 137 | 229-236
Article title

Solution of linear systems of differential equations with singular constant coefficients by the Drazin inverse of matrices

Content
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Languages of publication
EN
Abstracts
EN
Let A ,B be n×n matrices of complex numbers. Let G a vector-valued function of the real variable t. A and B may both be singular, rank(A) = 1, and the trac of A is not equal zero. The linear system of differential equations Ax^' (t)+Bx(t)=G(t) is studied using the Drazin inverse A^D of A, and a new matrix K∈C^(n×n). In this paper, we obtain a new closed form for the general solution of the differential system when the system is tractable.
Discipline
Year
Volume
137
Pages
229-236
Physical description
Contributors
  • Mathematics Department, Science Faculty, Sabratha University, Sabratha, Libya
  • Mathematics Department, Science Faculty, Sabratha University, Sabratha, Libya
References
  • S. L. Campbell, C. D. Meyer, Jr., Generalized Inverses of Linear Transformations, Pitman, London, 1979.
  • S. L. Campbell, C. D. Meyer, Jr., and N. J. Rose, Application of the Drazin Invese to Linear Systems of Differential Equations with Singular Constant Coefficients, SIAM J. Appl. Math. 31 (1976) 411-425.
  • C. Bu, K. Zhang, J. Zhao, Representation of the Drazin inverse on solution of a class singular differential equations. Linear and Multilinear Algebra, 59 (2011) 863-877.
  • N. Castro-Gonz'alez, E. Dopazo, Representation of the Drazin inverse for a class of block matrices. Linear Algebra Appl. 400 (2005) 253-269.
  • R. Hartwing, X. Li, Y. Wei., Representation for the Drazin inverse of a 2×2 block matrix. SIAM J. Matrix Anal. Appl. 27 (2006) 757-771.
  • A. Ben-Israel, T. N. E. Greville, Generalized inverses: Theory and Applications, Wiley, New York (1974).
  • J. H. Wilkinson, Note on the practical significance of the Drazin inverse, Stanford University, England, Stan-CS-79-736, 1979.
Document Type
short_communication
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-7bff69a1-c871-47b6-8005-dbbafa0bb39c
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