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Abstract
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| In this paper we study the generalized Drazin inverse of the sum of two elements in a Banach algebra, and we obtain a representation for the Drazin inverse of a+b under new conditions which relax the condition ab=0. Our approach is based on a representation for the resolvent of a 2x2 matrix with entries in a Banach algebra, which we provide, and the Laurent expansion of the resolvent in terms of the generalized Drazin inverse. Our results can be applied to obtain different representations of the generalized Drazin inverse of block matrices, under certain conditions, in terms of the individual blocks. We extend the result of Meyer and Rose for the Drazin inverse of a block triangular matrix. Finally, we present a numerical example for the Drazin inverse of 2x2 block matrices over the complex numbers. | |
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International
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Si |
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Congress
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15-th Conference of the International Linear Algebra Society ILAS 2008 |
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960 |
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Place
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Cancún |
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Reviewers
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Si |
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ISBN/ISSN
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Start Date
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16/06/2008 |
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End Date
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20/06/2008 |
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From page
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11 |
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To page
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11 |
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Abstracts 15-th Conference of the International Linear Algebra Society |