Integral representation of the Drazin inverse
نویسندگان
چکیده
منابع مشابه
Full-rank and Determinantal Representation of the Drazin Inverse
In this article we introduce a full-rank representation of the Drazin inverse AD of a given complex matrix A, which is based on an arbitrary full-rank decomposition of Al, l ≥ k, where k is the index of A. We show that the known representation of the Drazin inverse of A, devised in [7], represents a partial case of this result. Using this general representation, we introduce a determinantal rep...
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In this paper we study the W -weighted Drazin inverse of the bounded linear operators between Banach spaces and its representation theorem. Based on this representation, utilizing the spectral theory of Banach space operators, we derive an approximating expression of the W -weighted Drazin inverse and an error bound. Also, a perturbation theorem for the W -weighted Drazin inverse is uniformly o...
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Several representations of the generalized Drazin inverse of an anti-triangular block matrix in Banach algebra are given in terms of the generalized Banachiewicz--Schur form.
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A new result on the Drazin inverse of 2× 2 block matrix M = [ A B D C ] , where A and C are square matrices are presented, extended in the case when D = 0, the well known representation for the Drazin inverse of M , given by Hartwig, Meyer and Rose in 1977, respectively. Using that new result, an explicit representation for the Drazin inverse of a modified matrix P + RS and its generalized matr...
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We present a unified representation theorem for the Drazin inverse of linear operators in Hilbert space and a general error bound. Five specific expressions, computational procedures, and their error bounds for the Drazin inverse are uniformly derived from the unified representation theorem. 2002 Elsevier Science Inc. All rights reserved.
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