Result: Representations of the Drazin inverse for a class of block matrices
Title:
Representations of the Drazin inverse for a class of block matrices
Authors:
Source:
Linear Algebra and its Applications. 400:253-269
Publisher Information:
Elsevier BV, 2005.
Publication Year:
2005
Subject Terms:
index, Block matrix, Numerical Analysis, Algebra and Number Theory, binomial coefficients, block matrix, 01 natural sciences, Index, Binomial coefficients, Discrete Mathematics and Combinatorics, Theory of matrix inversion and generalized inverses, Drazin inverse, Geometry and Topology, 0101 mathematics
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0024-3795
DOI:
10.1016/j.laa.2004.12.027
Access URL:
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....a72309d3cebc76aa892e4e776820caae
Database:
OpenAIRE
Further Information
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 \(A\)).