Characterizations of a class of matrices and perturbation of the Drazin inverse

Castro González, Nieves and Robles Santamarta, Juan and Vélez Cerrada, José Ygnacio (2008). Characterizations of a class of matrices and perturbation of the Drazin inverse. "Siam Journal on Matrix Analysis and Applications", v. 30 (n. 2); pp. 882-897. ISSN 0895-4798.

Description

Title: Characterizations of a class of matrices and perturbation of the Drazin inverse
Author/s:
  • Castro González, Nieves
  • Robles Santamarta, Juan
  • Vélez Cerrada, José Ygnacio
Item Type: Article
Título de Revista/Publicación: Siam Journal on Matrix Analysis and Applications
Date: September 2008
ISSN: 0895-4798
Volume: 30
Subjects:
Faculty: Facultad de Informática (UPM)
Department: Matemática Aplicada
UPM's Research Group: singular matrix, Drazin inverse, eigenprojectors, perturbation
Creative Commons Licenses: Recognition - No derivative works - Non commercial

Full text

[img]
Preview
PDF - Requires a PDF viewer, such as GSview, Xpdf or Adobe Acrobat Reader
Download (215kB) | Preview

Abstract

Este trabajo supone un avance en la caracterización y representación de una clase de matrices perturbadas, para el estudio de la perturbación de la inversa de Drazin. Se obtienen diversas caracterizaciones de las matrices perturbadas: geométrica, algebraica, en función de los rangos, y respecto una representación matricial por bloques. Con estas caracterizaciones se alcanzan expresiones explícitas de la inversa de Drazin de la matriz perturbada, y cotas del error relativo de la perturbación de la inversa de Drazin. Se presentan ejemplos numéricos en los que se comparan las cotas dadas con otras publicadas recientemente en la literatura. Como aplicación, se presentan resultados relativos a la continuidad de la inversa de Drazin. Given a singular square matrix $A$ with index $r$, $\operatorname{ind}(A)=r$, we establish several characterizations in the Drazin inverse framework of the class of matrices $B$, which satisfy the conditions $\mathcal{N}(B^s)\cap\mathcal{R}(A^r)=\{0\}$ and $\mathcal{R}(B^s)\cap\mathcal{N}(A^r)=\{0\}$ with $\operatorname{ind}(B)=s$, where $\mathcal{N}(A)$ and $\mathcal{R}(A)$ denote the null space and the range space of a matrix $A$, respectively. We give explicit representations for $B^{\rm D}$ and $BB^{\rm D}$ and upper bounds for the errors $\|B^{\rm D}-A^{\rm D}\|/\|A^{\rm D}\|$ and $\|BB^{\rm D}-AA^{\rm D}\|$. In a numerical example we show that our bounds are better than others given in the literature.

More information

Item ID: 2159
DC Identifier: http://oa.upm.es/2159/
OAI Identifier: oai:oa.upm.es:2159
Official URL: http://scitation.aip.org/dbt/dbt.jsp?KEY=SJMAEL&Volume=30&Issue=2
Deposited by: Memoria Investigacion
Deposited on: 01 Feb 2010 10:56
Last Modified: 20 Apr 2016 11:55
  • Logo InvestigaM (UPM)
  • Logo GEOUP4
  • Logo Open Access
  • Open Access
  • Logo Sherpa/Romeo
    Check whether the anglo-saxon journal in which you have published an article allows you to also publish it under open access.
  • Logo Dulcinea
    Check whether the spanish journal in which you have published an article allows you to also publish it under open access.
  • Logo de Recolecta
  • Logo del Observatorio I+D+i UPM
  • Logo de OpenCourseWare UPM