Solution of linear systems of differential equations with singular constant coefficients by the Drazin inverse of matrices
Languages of publication
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.
- 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.
Publication order reference