Results 11 to 20 of about 340 (155)
The Expression of the Generalized Drazin Inverse of A−CB [PDF]
Abstract and Applied Analysis, 2012 We investigate the generalized Drazin inverse of A−CB over Banach spaces stemmed from the Drazin inverse of a modified matrix and present its expressions under some conditions.
Xiaoji Liu, Dengping Tu, Yaoming Yu
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Jacobson’s lemma for the generalized Drazin inverse
Linear Algebra and its Applications, 2012 0truemm0truemm We study properties of elements in a ring which admit the generalized Drazin inverse. It is shown that the element 1-ab is generalized Drazin invertible if and only if so is 1-ba and a formula for the generalized Drazin inverse of 1-ba in ...
Chen, Jianlong +5 more
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Formulae for the Generalized Drazin Inverse of a Block Matrix in Banach Algebras [PDF]
Journal of Function Spaces, 2015 We present some new representations for the generalized Drazin inverse of a block matrix in a Banach algebra under conditions weaker than those used in resent papers on the subject.
Xiaoji Liu, Xiaolan Qin
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A Seventh-Order Scheme for Computing the Generalized Drazin Inverse
Mathematics, 2019 One of the most important generalized inverses is the Drazin inverse, which is defined for square matrices having an index. The objective of this work is to investigate and present a computational tool in the form of an iterative method for computing ...
Dilan Ahmed +3 more
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A generalization of the generalized Drazin inverse in rings
Journal of Algebra and Its ApplicationsThe notions of (quasi-) polarity and (generalized) Drazin invertibility of an element a in a ring R, defined upon the set of (quasi-) nilpotent elements, are extended by using the set ∇(R) = {a ∈ R : 1 − au is unit in R for all unit u ∈ R with ua = au ...
Quynh, Truong Cong +3 more
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Representations for the generalized Drazin inverse in a Banach algebra [PDF]
, 2013 [EN] In this paper, we investigate additive properties for the generalized Drazin inverse in a Banach algebra A. We give some representations for the generalized Drazin inverse of a+b, where a and b are elements of A under some new conditions, extending
Benítez López, Julio, Qin, Y., Liu, X.
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On continuity of the Moore-Penrose and Drazin generalized inverses
Linear Algebra and its Applications, 1977 Let A be an m × n matrix. It is shown that if a matrix  comes close to satisfying the definition of the Moore-Penrose generalized inverse of A,A†, then ┆–A†┆ is small. Norm estimates are given which make precise what is close.
Campbell, Stephen L.
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Extension of generalized strong Drazin inverse [PDF]
Operators and Matrices, 2021 Summary: As an extension of the generalized strong Drazin inverse, we present a new generalized inverse for Banach algebra elements based on a \(g\)-Drazin invertible element rather than on a quasinilpotent element in the definition of the generalized strong Drazin inverse.
Mosić, Dijana, Zou, Honglin
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Perturbation of the generalized Drazin inverse [PDF]
The Electronic Journal of Linear Algebra, 2010 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.
Chunyuan Deng, Yimin Wei
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Dual Drazin generalized inverse for dual matrices
CoRR, 2023 Under certain necessary and sufficient conditions, we establish the existence of the DDGI of a dual matrix of any ...
Amit Kumar, Vaibhav Shekhar
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