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In this paper, we revise the core EP inverse of a square matrix introduced by Prasad and Mohana in [12], Core EP inverse, Linear and Multilinear Algebra62(3) (2014), 792-802. Firstly, we give a new representation and a new charact...
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In this paper, we revise the core EP inverse of a square matrix introduced by Prasad and Mohana in [12], Core EP inverse, Linear and Multilinear Algebra62(3) (2014), 792-802. Firstly, we give a new representation and a new characterization of the core EP inverse. Then, we study some properties of the core EP inverse by using a representation by block matrices. Secondly, we extend the notion of core EP inverse to rectangular matrices by means of a weighted core EP decomposition. Finally, we study some properties of weighted core EP inverses.
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In this note, we present a unified representation and an approximation theorem for the outer inverse A (2) of a matrix A, which is the matrix X satisfying XAX = X, T,S R(X) = T, N(X) = S. Based on the new approximation theorem, we...
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In this note, we present a unified representation and an approximation theorem for the outer inverse A (2) of a matrix A, which is the matrix X satisfying XAX = X, T,S R(X) = T, N(X) = S. Based on the new approximation theorem, we can develop several (2) expressions and computational procedures for the generalized inverse A(T,S)((2)), which im prove the recent work on this topic. (C) 2002 Elsevier Inc. All rights reserved. [References: 20]
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In this article we formulate basic results on outer generalized inverses of elements in rings. We characterize elements which have the same idempotents related to their particular outer generalized inverses and investigate positiv...
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In this article we formulate basic results on outer generalized inverses of elements in rings. We characterize elements which have the same idempotents related to their particular outer generalized inverses and investigate positive generalized inverses in C*-algebras.
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In this paper, we investigate stable perturbations and their characterizations for various types of outer inverses, such as generalized, {2,3}-, {2,4}-, {2,5}-, {1,2,3}-, {1,2,4}-, Moore-Penrose, group, Drazin and generalized Draz...
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In this paper, we investigate stable perturbations and their characterizations for various types of outer inverses, such as generalized, {2,3}-, {2,4}-, {2,5}-, {1,2,3}-, {1,2,4}-, Moore-Penrose, group, Drazin and generalized Drazin inverses. Some known results are improved and extended.
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For given complex matrix A and nonzero complex vectors b, c, relationships between generalized inverses of A and generalized inverses of the rank-one-modified matrix M = A + bc* (with c* being the conjugate transpose of c) are inv...
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For given complex matrix A and nonzero complex vectors b, c, relationships between generalized inverses of A and generalized inverses of the rank-one-modified matrix M = A + bc* (with c* being the conjugate transpose of c) are investigated. The following three questions are considered: (i) when a given generalized inverse A(-) belongs to the set M{1} of all generalized inverses of M, (ii) when does A(-) epsilon A{1} exist such that simultaneously A(-) epsilon M{1}, and (iii) when the set A{1} is a subset of M{1}. The same questions are also discussed for reflexive generalized inverses of A and M. The answers obtained are commented from the view-point of a result concerning comparison of ranks of M and A. (C) 2004 Elsevier Inc. All rights reserved.
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The weighted generalized inverse has several important applications in the theoretical research and numerical computations. In this paper, we present a representation for the weighted generalized inverse of the product of two matrices A and B.
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in this article we characterize operators on Banach spaces which have the same projections related to their outer or inner generalized inverses. As corollaries, we obtain well-known results for the Drazin inverse of bounded operat...
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in this article we characterize operators on Banach spaces which have the same projections related to their outer or inner generalized inverses. As corollaries, we obtain well-known results for the Drazin inverse of bounded operators. (C) 2003 Elsevier Inc. All rights reserved.
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The problem of developing conditions under which generalized inverses of a partitioned matrix can be expressed in the so-called Banachiewicz-Schur form is reconsidered. Theorem of Marsaglia and Styan [Sankhya Ser. A 36 (1974) 437]...
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The problem of developing conditions under which generalized inverses of a partitioned matrix can be expressed in the so-called Banachiewicz-Schur form is reconsidered. Theorem of Marsaglia and Styan [Sankhya Ser. A 36 (1974) 437], concerning the class of all generalized inverses, the class of reflexive generalized inverses, and the Moore-Penrose inverse, is strengthened and new results are established for the classes of outer inverses, least-squares generalized inverses, and minimum norm generalized inverses. (C) 2002 Elsevier Science Inc. All rights reserved. [References: 2]
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This paper presents a recurrent neural network (RNN) for computing the Drazin inverse of a real matrix in real time. This recurrent neural network (RNN) is composed of independent parts (subnetworks), where is the order of the i...
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This paper presents a recurrent neural network (RNN) for computing the Drazin inverse of a real matrix in real time. This recurrent neural network (RNN) is composed of independent parts (subnetworks), where is the order of the input matrix. These subnetworks can operate concurrently, so parallel and distributed processing can be achieved. In this way, the computational advantages over the existing sequential algorithms can be attained in real-time applications. The RNN defined in this paper is convenient for an implementation in an electronic circuit. The number of neurons in the neural network is the same as the number of elements in the output matrix, which represents the Drazin inverse. The difference between the proposed RNN and the existing ones for the Drazin inverse computation lies in their network architecture and dynamics. The conditions that ensure the stability of the defined RNN as well as its convergence toward the Drazin inverse are considered. In addition, illustrative examples and examples of application to the practical engineering problems are discussed to show the efficacy of the proposed neural network.
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摘要 :
We study the weighted outer generalized inverse of a given operator between Banach spaces, as well as weighted outer generalized inverses of elements in rings and Banach algebras.
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