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Erschienen in: Journal of Applied Mathematics and Computing 1-2/2012

01.10.2012 | Original Research

Group inverse for a class of 2×2 anti-triangular block matrices over skew fields

verfasst von: Chongguang Cao, Chunjie Zhao

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2012

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Abstract

Suppose K is a skew field. Let K m×n denote the set of all m×n matrices over K. In this paper, we give necessary and sufficient conditions for the existence and explicit representations of the group inverses of the block matrices https://static-content.springer.com/image/art%3A10.1007%2Fs12190-012-0555-y/MediaObjects/12190_2012_555_IEq1_HTML.gif in the following three cases, respectively:
(i)
\(\mathrm{rank}(S)=\mathrm{rank}(B^{\pi}A)\);
 
(ii)
\(\mathrm{rank}(S)=\mathrm{rank}(AB^{\pi})\);
 
(iii)
\(\mathrm{rank}(S)=\mathrm{rank}(B^{\pi}A)=\mathrm{rank}(AB^{\pi})\),
 
where A,B,CK n×n , B # exists, R(B)=R(C), N(B)=N(C) and S=B π AB π . The paper’s conclusions generalized some related results of Zhao and Bu (Electron. J. Linear Algebra 21:63–75, 2010).

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Metadaten
Titel
Group inverse for a class of 2×2 anti-triangular block matrices over skew fields
verfasst von
Chongguang Cao
Chunjie Zhao
Publikationsdatum
01.10.2012
Verlag
Springer-Verlag
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2012
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-012-0555-y

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Preface