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Erschienen in: Journal of Applied Mathematics and Computing 1-2/2013

01.07.2013 | Applied mathematics

Group inverse for two classes of 2×2 anti-triangular block matrices over right Ore domains

verfasst von: Yanling Ge, Hanyu Zhang, Yuqiu Sheng, Chongguang Cao

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2013

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Abstract

Suppose ℜ is a right Ore domain with identity 1. Let ℜ m×n denote the set of all m×n matrices over ℜ. In this paper, we give the 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%2Fs12190-012-0636-y/MediaObjects/12190_2012_636_IEq1_HTML.gif in the following two cases, respectively:
(i)
A 2=A and CA=C;
 
(ii)
r(C)≤r(B) and A=DC,
 
where A∈ℜ n×n , B∈ℜ n×m , C∈ℜ m×n , D∈ℜ n×m . The paper’s results generalize some relative results of Liu and Yang (Appl. Math. Comput. 218:8978–8986, 2012).

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Metadaten
Titel
Group inverse for two classes of 2×2 anti-triangular block matrices over right Ore domains
verfasst von
Yanling Ge
Hanyu Zhang
Yuqiu Sheng
Chongguang Cao
Publikationsdatum
01.07.2013
Verlag
Springer-Verlag
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2013
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-012-0636-y

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