Perturbation of the generalized Drazin inverse
نویسندگان
چکیده
منابع مشابه
Ela Perturbation of the Generalized Drazin Inverse
In this paper, we investigate the perturbation of the generalized Drazin invertible matrices and derive explicit generalized Drazin inverse expressions for the perturbations under certain restrictions on the perturbing matrices.
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†Department of Mathematics, Southeast University, Nanjing 210096, China ‡College of Mathematics and Information Science, Guangxi University, Nanning 530004, China E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] Abstract: It is well known that for an associative ring R, if ab is Drazin invertible then ba is Drazin invertible. In this case, (ba)D = b((ab)D)2a. This for...
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K e y w o r d s I n d e x , Drazin inverse, Group inverse, Per turbat ion bound, Core rank. 1. I N T R O D U C T I O N A necessary and sufficient condition for the continuity of the Drazin inverse (to be defined in the next section) was established by Campbell and Meyer in 1975 [1]. They stated the main result: suppose tha t Aj, j = 1, 2 , . . . , and A are n × n matrices such tha t A j ~ A . T...
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Let A denote a square complex matrix and let E be a perturbation matrix. The purpose of this paper is to investigate the perturbation of the Drazin inverse when B = A + E satisfies the rank conditions rankA = rankB = rankAB, where r and s denote the indices of A and B, respectively. We will derive an explicit representation of B as a function of A and B −A , for certain positive integers j, k. ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2010
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1416