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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Bibliographic Details
Published inLinear & multilinear algebra Vol. 55; no. 2; pp. 103 - 112
Main Authors Koliha, J. J., RakoČević, V.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.03.2007
Subjects
2000 Mathematics Subject Classifications: 46L05
C-algebra
Idempotent
Moore-Penrose inverse
Range projection
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Summary: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.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081080500472954