290 research outputs found
Some additive results on Drazin inverse
In this paper, we investigate additive results of the Drazin inverse of elements in
a ring R. Under the condition ab = ba, we show that a + b is Drazin invertible if and only if aa^D(a+b) is Drazin invertible, where the superscript D means the Drazin inverse. Furthermore we find an expression of (a + b)^D. As an application we give some new representations for the Drazin inverse of a 2 Ć 2 block matrix.Supported by the National Natural Science Foundation of China (11361009), the Guangxi Provincial Natural Science Foundation of China (2013GXNSFAA019008), and Science Research Project 2013 of the China-ASEAN Study Center (Guangxi Science Experiment Center) of Guangxi University for Nationalities.Liu, X.; Qin, X.; BenĆtez LĆ³pez, J. (2015). Some additive results on Drazin inverse. Applied Mathematics - A Journal of Chinese Universities. 30(4):479-490. https://doi.org/10.1007/s11766-015-3333-4S479490304A Ben-Israel, T N E Greville. Generalized Inverses, Theory and Applications, 2nd edition, Springer-Verlag, 2003.S L Campbell, C D Meyer. Generalized Inverses of Linear Transformations, Pitman (Advanced Publishing Program), Boston, MA, 1979.N Castro-GonzĆ”lez, J J Koliha. Additive perturbation results for the Drazin inverse, Linear Algebra Appl, 2005, 397: 279ā297.N Castro-GonzĆ”lez, E Dopazo, M F MartĆnez-Serrano. On the Drazin inverse of the sum of two operators and its application to operator matrices, J Math Anal Appl, 2008, 350: 207ā215.N Castro-GonzĆ”lez, M F MartĆnez-Serrano. Expressions for the g-Drazin inverse of additive perturbed elements in a Banach algebra, Linear Algebra Appl, 2010, 432: 1885ā1895.N Castro-GonzĆ”lez, J J Koliha. New additive results for the Drazin inverse, Proc Roy Soc Edinburgh Sect A, 2004, 134: 1085ā1097.M Catral, D D Olesky, P van den Driessche. Block representations of the Drazin inverse of a bipartite matrix, Electron J Linear Algebra, 2009, 18: 98ā107.J L Chen, G F Zhuang, Y Wei. The Drazin inverse of a sum of morphisms, Acta Math Sci Ser A Chin Ed, 2009, 29(3): 538ā552.D S CvetkoviÄ-IliÄ, D S DjordjeviÄ, Y Wei. Additive results for the generalized Drazin inverse in a Banach algebra, Linear Algebra Appl, 2006, 418, 53ā61.D S CvetkoviÄ-IliÄ. A note on the representation for the Drazin inverse of 2 Ć 2 block matrices, Linear Algebra Appl, 2008, 429: 242ā248.C Deng. The Drazin inverses of sum and difference of idempotents, Linear Algebra Appl, 2009, 430: 1282ā1291.C Deng, Y Wei. Characterizations and representations of the Drazin inverse of idempotents, Linear Algebra Appl, 2009, 431: 1526ā1538.C Deng, Y Wei. New additive results for the generalized Drazin inverse, J Math Anal Appl, 2010, 370: 313ā321.D S DjordjeviÄ, P S StanimiroviÄ. On the generalized Drazin inverse and generalized resolvent, Czechoslovak Math J, 2001, 51(126): 617ā634.D S DjordjeviÄ, Y Wei. Additive results for the generalized Drazin inverse, J Aust Math Soc, 2002, 73: 115ā125.D S DjordjeviÄ, V RakoÄeviÄ. Lectures on Generalized inverses, University of NiÅ”, 2008.E Dopazo, M F MartĆnez-Serrano. Further results on the representation of the Drazin inverse of a 2 Ć 2 block matrices, Linear Algebra Appl, 2010, 432: 1896ā1904.M P Drazin. Pseudo-inverses in associative rings and semiproup, Amer Math Monthly, 1958, 65: 506ā514.R E Hartwig, G R Wang, Y Wei. Some additive results on Drazin inverse, Linear Algebra Appl, 2001, 322: 207ā217.R E Hartwig, X Li, Y Wei. Representations for the Drazin inverse of a 2Ć2 block matrix, SIAM J Matrix Anal Appl, 2006, 27: 757ā771.Y Liu, C G Cao. Drazin inverse for some partitioned matrices over skew fields, J Nat Sci Heilongjiang Univ, 2004, 24: 112ā114.J LjubisavljeviÄ, D S CvetkoviÄ-IliÄ. Additive results for the Drazin inverse of block matrices and applications, J Comput Appl Math, 2011, 235: 3683ā3690.C D Meyer ffixJr, N J Rose. The index and the Drazin inverse of block triangular matrices, SIAM J Appl Math, 1977, 33(1): 1ā7.L Wang, H H Zhu, X Zhu, J L Chen. Additive property of Drazin invertibility of elements, arXiv: 1307.1816v1 [math.RA], 2013.H Yang, X Liu. The Drazin inverse of the sum of two matrices and its applications, J Comput Appl Math, 2011, 235: 1412ā1417
Representations for generalized Drazin inverse of operator matrices over a Banach space
In this paper we give expressions for the generalized Drazin inverse of a
(2,2,0) operator matrix and a operator matrix under certain
circumstances, which generalizes and unifies several results in the literature
Computing generalized inverses using LU factorization of matrix product
An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and
the Moore-Penrose inverse of a given rational matrix A is established. Classes
A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R*
and T*(AT*)+, where R and T are rational matrices with appropriate dimensions
and corresponding rank. The proposed algorithm is based on these general
representations and the Cholesky factorization of symmetric positive matrices.
The algorithm is implemented in programming languages MATHEMATICA and DELPHI,
and illustrated via examples. Numerical results of the algorithm, corresponding
to the Moore-Penrose inverse, are compared with corresponding results obtained
by several known methods for computing the Moore-Penrose inverse
ADDITIVE PROPERTIES OF THE DRAZIN INVERSE FOR MATRICES AND BLOCK REPRESENTATIONS: A SURVEY
In this paper, a review of a development of the Drazin inverse for the sumĀ of two matrices has been given. Since this topic is closely related to the problem ofĀ finding the Drazin inverse of a 2x2 block matrix, the paper also offers a survey of this subject
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