Drazin inverse
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Bordering method to compute Core-EP inverse Open
Following the work of Kentaro Nomakuchi[10] and Manjunatha Prasad et.al., [7] which relate various generalized inverses of a given matrix with suitable bordering,we describe the explicit bordering required to obtain core-EP inverse, core-E…
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The DMP inverse for rectangular matrices Open
The definition of the DMP inverse of a square matrix with complex elements is extended to rectangular matrices by showing that for any A and W, m by n and n by m, respectively, there exists a unique matrix X, such that XAX = X, XA = Wad, w…
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Determinantal Representations of the Core Inverse and Its Generalizations with Applications Open
In this paper, we give the direct method to find of the core inverse and its generalizations that is based on their determinantal representations. New determinantal representations of the right and left core inverses, the right and left co…
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Representations and properties of the <i>W</i>-weighted core-EP inverse Open
In this paper, we investigate the weighted core-EP inverse introduced by Ferreyra, Levis and Thome. Several computational representations of the weighted core-EP inverse are obtained in terms of singular-value decomposition, full-rank deco…
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The inverse along an element in rings Open
[EN] Several properties of the inverse along an element are studied in the context of unitary rings. New characterizations of the existence of this inverse are proved. Moreover, the set of all invertible elements along a fixed element is f…
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*-DMP elements in *-semigroups and *-rings Open
In this paper, we investigate *-DMP elements in *-semigroups and *-rings. The notion of *-DMP element was introduced by Patr?cio and Puystjens in 2004. An element a is *-DMP if there exists a positive integer m such that am is EP. We first…
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New extensions of Cline’s formula for generalized inverses Open
In this paper, Cline?s formula for the well-known generalized inverses such as Drazin inverse, pseudo Drazin inverse and generalized Drazin inverse is extended to the case when ( acd = dbd dba = aca. Also, applications are given to some in…
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Explicit formulae for the generalized drazin inverse of block matrices over a Banach algebra Open
In this paper, we give expressions for the generalized Drazin inverse of a (2,2,0) block matrix over a Banach algebra under certain circumstances, utilizing which we derive the generalized Drazin inverse of a 2x2 block matrix in a Banach a…
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A class of Drazin inverses in rings Open
A strongly direct sum decomposition given by a strongly nil-clean endomorphism motivates us to introduce a class of new Drazin inverses, which is called strong Drazin inverse. In this paper, some basic properties of the strong Drazin inver…
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New additive results for the generalized Drazin inverse in a Banach algebra Open
In this paper, we investigate additive properties of the generalized Drazin inverse in a Banach algebra A. We find explicit expressions for the generalized Drazin inverse of the sum a + b, under new conditions on a,b ? A.
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Generalized Inverses Estimations by Means of Iterative Methods with Memory Open
A secant-type method is designed for approximating the inverse and some generalized inverses of a complex matrix A. For a nonsingular matrix, the proposed method gives us an approximation of the inverse and, when the matrix is singular, an…
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Drazin inverse matrix method for fractional descriptor discrete-time linear systems Open
The Drazin inverse of matrices is applied in order to find the solutions of the state equations of fractional descriptor discrete-time linear systems. The solution of the state equation is derived and the set of consistent initial conditio…
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On the pseudo drazin inverse of the sum of two elements in a Banach algebra Open
In this paper, some additive properties of the pseudo Drazin inverse are obtained in a Banach algebra. In addition, we find some new conditions under which the pseudo Drazin inverse of the sum a + b can be explicitly expressed in terms of …
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Cline’s formula for g-Drazin inverses in a ring Open
It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in m…
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Weighted G-Drazin inverse for operators on Banach spaces Open
We define an extension of weighted G-Drazin inverses of rectangular matrices to operators between two Banach spaces. Some properties of weighted G-Drazin inverses are generalized and some new ones are proved. Using weighted G-Drazin invers…
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A Rank-Preserving Generalized Matrix Inverse for Consistency With Respect to Similarity Open
There has recently been renewed recognition of the need to understand the\nconsistency properties that must be preserved when a generalized matrix inverse\nis required. The most widely known generalized inverse, the Moore-Penrose\npseudoin…
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Block representations for the Drazin inverse of anti-triangular matrices Open
The paper is devoted to the study of the Drazin inverse of some structured matrices that appear in applications. We focus mainly on deriving formulas for the Drazin inverse of an anti-triangular block matrix M in terms of its blocks. New r…
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Generalized weighted core inverse in Banach *-algebras Open
In this paper, we introduce the notion of the generalized weighted core inverse in a Banach algebra. We characterize this new generalized inverse by using the generalized weighted core decomposition and present the representations by the g…
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Representations of the (b,c)-inverses in rings with involution Open
Let R be a ring and b,c ? R. The concept of (b,c)-inverses was introduced by Drazin in 2012. In this paper, the existence and the expression of the (b,c)-inverse in a ring with an involution are investigated. A new representation of the (b…
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On the (b,c)-inverse in rings Open
We present new characterizations for the existence of the (b,c)-inverse in a ring. The set of all (b,c)-invertible elements is described too. Necessary and sufficient conditions which ensure that the (b,c)-inverse of a given element commut…
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Formulas for the Drazin inverse of matrices over skew fields Open
For two square matrices P and Q over skew fields, the explicit formulas for the Drazin inverse of P+Q are given in the cases of (i) PQ2=0, P2QP=0, (QP)2=0; (ii) P2QP=0, P3Q=0, Q2=0, which extend the results in [M.F. Mart?nez-Serrano et al.…
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Generalized Drazin inverses in a ring Open
An element a in a ring R has generalized Drazin inverse if and only if there exists b ? comm2(a) such that b = b2a,a-a2b ? Rqnil. We prove that a ? R has generalized Drazin inverse if and only if there exists p3 = p ? comm2(a) such that a …
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Minimal rank weak Drazin inverses: a class of outer inverses with prescribed range Open
For any square matrix $A$, it is proved that minimal rank weak Drazin inverses (Campbell and Meyer, 1978) of $A$ coincide with outer inverses of $A$ with range $\mathcal{R}(A^{k})$, where $k$ is the index of $A$. It is shown that the minim…
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Generalizations of some conditions for Drazin inverses of the sum of two matrices Open
In this article, we present some formulas of the Drazin inverses of the sum of two matrices under the conditions P2QP = 0, P2Q2 = 0, QPQ = 0 and PQP2 = 0, PQ2 = 0, QP3 = 0 respectively. These conditions are weaker than those used in some l…
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The perturbation bound for the T-Drazin inverse of tensor and its application Open
In this paper, let A and B be n x n x p complex tensors and B = A + E. Denote the T-Drazin inverse of A by AD. We give a perturbation bound for ||BD-AD||=||AD|| under condition (W). Considering the solution of singular tensor equation A* x…
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Dual Drazin inverses of dual matrices and dual Drazin-inverse solutions of systems of linear dual equations Open
In this paper, we study a kind of dual generalized inverse, which is called the dual Drazin inverse. Unlike the real matrices case, the dual Drazin inverse of a square dual matrix may not exist. It is shown that the dual Drazin inverse is …
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The representations of the g-Drazin inverse in a Banach algebra Open
The aim of this paper is to establish an explicit representation of the generalized Drazin inverse $(a+b)^d$ under the condition $$ab^2=0, ba^2=0, a^{\pi}b^{\pi}(ba)^2=0.$$ Furthermore, we apply our results to give some representation of g…
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On generalized core-EP invertibility in a Banach algebra Open
We present new properties of generalized core-EP inverse in a Banach *-algebra. We characterize this new generalized inverse by using involved annihilators. The generalized core-EP inverse for products is obtained. The core-EP orders for B…
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Some additive results for the Drazin inverse and its application Open
In this paper, we give some formulas for the Drazin inverses of the sum of two matrices under conditions weaker than those used in some current literature. Also, we obtain representation for the Drazin inverse of a complex block matrix und…
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Drazin inverse matrix method for fractional descriptor discrete-time linear systems Open
The Drazin inverse of matrices is applied in order to find the solutions of the state equations of fractional descriptor discrete-time linear systems.The solution of the state equation is derived and the set of consistent initial condition…