Representations of the Drazin inverse for a class of block matrices
type: Item
instance of: scholarly article
title: Representations of the Drazin inverse for a class of block matrices
zbMATH Open document ID: 1076.15007
author: Niranjan Chakravarthy
published in: Linear Algebra and its Applications
publication date: 2005-06-01T00:00:00Z
review text: The paper presents a formula for the Drazin inverse of the block matrix \( F=\left(\begin{smallmatrix} I_{d} & I_{d} \\ E & 0 \end{smallmatrix}\right)\), where \(E\in \mathbb{C} ^{d\times d}\), ind\(( E) =r\). Further, it gives a representation of the Drazin inverse of \(M=\left(\begin{smallmatrix} A & B \\ C & 0_{d,d} \end{smallmatrix}\right),\) where \(A\in \mathbb{C} ^{d\times d}\), \(B\in \mathbb{C} ^{d\times ( n-d) }\), \(C\in \mathbb{C} ^{( n-d) \times d}\) and \(CA^{D}A=C,A^{D}BC=BCA^{D}\) (\(A^{D}\) denotes the Drazin inverse of \(A\)).
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 2173028
zbMATH Keywords: Drazin inverse
zbMATH Keywords: index
zbMATH Keywords: binomial coefficients
zbMATH Keywords: block matrix
reviewed by: Nicholas Karampetakis
MaRDI profile type: Publication
full work available at URL: j.laa.2004.12.027
OpenAlex ID: W2088994249
cites work: The Drazln inverse and systems of second order linear differential equations
cites work: Q4002435
cites work: A Drazin inverse for rectangular matrices
cites work: On the spectrum and pseudoinverse of a special bordered matrix
cites work: On the Generalized Drazin Inverse and Generalized Resolvent
cites work: On Solving Block-Structured Indefinite Linear Systems
cites work: Q4950461
cites work: Some additive results on Drazin inverse
cites work: A note on preconditioning nonsymmetric matrices
cites work: The Index and the Drazin Inverse of Block Triangular Matrices
cites work: Q3216653
cites work: Expressions for the drazin inverse of a 2×2 Block Matrix
DOI: 10.1016/J.LAA.2004.12.027
description: scientific article; zbMATH DE number 2173028