Range projections and the Moore-Penrose inverse in rings with involution
In this article we study the existence of range projections in rings with involution, relating it to the existence of the Moore-Penrose inverse. The results are applied to the solution of the equation xbx = x in rings with involution, extending the results of Greville for matrices. Simpler new proof...
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| Published in | Linear & multilinear algebra Vol. 55; no. 2; pp. 103 - 112 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
01.03.2007
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| Subjects | |
| Online Access | Get full text |
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| Abstract | In this article we study the existence of range projections in rings with involution, relating it to the existence of the Moore-Penrose inverse. The results are applied to the solution of the equation xbx = x in rings with involution, extending the results of Greville for matrices. Simpler new proofs are given of the Moore-Penrose invertibility of regular elements in rings with involution, and of the Ljance's formula. |
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| AbstractList | In this article we study the existence of range projections in rings with involution, relating it to the existence of the Moore-Penrose inverse. The results are applied to the solution of the equation xbx = x in rings with involution, extending the results of Greville for matrices. Simpler new proofs are given of the Moore-Penrose invertibility of regular elements in rings with involution, and of the Ljance's formula. |
| Author | RakoČević, V. Koliha, J. J. |
| Author_xml | – sequence: 1 givenname: J. J. surname: Koliha fullname: Koliha, J. J. email: j.koliha@ms.unimelb.edu.au organization: Department of Mathematics and Statistics , The University of Melbourne – sequence: 2 givenname: V. surname: RakoČević fullname: RakoČević, V. organization: Faculty of Science and Mathematics , University of Niš |
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| CitedBy_id | crossref_primary_10_1016_j_amc_2020_125832 crossref_primary_10_1016_j_laa_2009_09_024 crossref_primary_10_1007_s40840_015_0242_x crossref_primary_10_1007_s10114_023_1439_9 crossref_primary_10_5402_2011_846165 crossref_primary_10_1016_j_laa_2009_02_032 crossref_primary_10_1080_03081087_2011_605064 crossref_primary_10_1016_j_amc_2011_06_040 crossref_primary_10_1016_j_laa_2008_05_012 crossref_primary_10_1016_j_amc_2015_07_057 crossref_primary_10_1016_j_laa_2015_02_017 |
| Cites_doi | 10.4064/sm-106-2-129-138 10.1216/rmjm/1181069874 10.2307/2695474 10.1515/dema-2001-0113 10.4064/sm-103-1-71-77 10.1137/0126074 10.1017/S0305004100030401 10.1080/030810802100023499 |
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| Copyright | Copyright Taylor & Francis Group, LLC 2007 |
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| SubjectTerms | 2000 Mathematics Subject Classifications: 46L05 C-algebra Idempotent Moore-Penrose inverse Range projection |
| Title | Range projections and the Moore-Penrose inverse in rings with involution |
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