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On the Moore-Penrose and the Drazin inverse of two projections on Hilbert space
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
Department of Mathematics, PMF Nis, Serbia.
2012 (English)Report (Other academic)
Abstract [en]

For two given orthogonal, generalized or hypergeneralized projectionsP and Q on Hilbert space H, we gave their matrix representation. We also gave canonical forms of the Moore-Penrose and the Drazin inverses of their product, difference and sum. In addition, it is showed when these operators are EP and some simple correlations between mentioned operators are established.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. , 16 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2012:03
Keyword [en]
Moore-penrose inverse, Drazin inverse, generalized projection, hypergeneralized projection
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-75869ISRN: LiTH-MAT-R–2012/03–SEOAI: oai:DiVA.org:liu-75869DiVA: diva2:509701
Available from: 2012-03-13 Created: 2012-03-13 Last updated: 2012-03-28Bibliographically approved
In thesis
1. Pairs of projections on a Hilbert space:properties and generalized invertibility
Open this publication in new window or tab >>Pairs of projections on a Hilbert space:properties and generalized invertibility
2012 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is concerned with the problem of characterizing sums, differences, and products of two projections on a separable Hilbert space. Other objective is characterizing the Moore-Penrose and the Drazin inverse for pairs of operators. We use reasoning similar to one presented in the famous P. Halmos’ two projection theorem: using matrix representation of two orthogonal projection depending on the relations between their ranges and null-spaces gives us simpler form of their matrices and allows us to involve matrix theory in solving problems. We extend research to idempotents, generalized and hypergeneralized projections and their combinations.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2012. 42 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1525
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-75909 (URN)978-91-7519-932-0 (ISBN)
Presentation
2012-04-16, Alan Turing, Building E, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2012-03-28 Created: 2012-03-16 Last updated: 2012-05-14Bibliographically approved

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Radosavljevic, Sonja

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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  • vancouver
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  • Other style
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Language
  • de-DE
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  • en-US
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  • Other locale
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Output format
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