Observatorio de I+D+i UPM

Memorias de investigación
Communications at congresses:
Representations for the generalized Drazin inverse of additive perturbations
Year:2008
Research Areas
  • Mathematics
Information
Abstract
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.
International
Si
Congress
15-th Conference of the International Linear Algebra Society ILAS 2008
960
Place
Cancún
Reviewers
Si
ISBN/ISSN
Start Date
16/06/2008
End Date
20/06/2008
From page
11
To page
11
Abstracts 15-th Conference of the International Linear Algebra Society
Participants
  • Autor: Maria Francisca Martinez Serrano (UPM)
  • Autor: Blanca Nieves Castro Gonzalez (UPM)
Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Sistemas Singulares e Inversas Generalizaciones
  • Departamento: Matemática Aplicada (Facultad de Informática)
S2i 2020 Observatorio de investigación @ UPM con la colaboración del Consejo Social UPM
Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
Cofinanciación del MINECO en el marco del Programa INNPACTO (IPT-020000-2010-22)