Ordered Structures and Projections
We associate a covering relation to the usual order relation defined in the set of all idempotent endomorphisms (projections) of a finite-dimensional vector space. A characterization is given of it. This characterization makes this order an order verifying the Jordan-Dedekind chain condition. We giv...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/783041 |
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| _version_ | 1850236846044348416 |
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| author | M. Yazi |
| author_facet | M. Yazi |
| author_sort | M. Yazi |
| collection | DOAJ |
| description | We associate a covering relation to the usual order relation defined in the set of all idempotent endomorphisms (projections) of a finite-dimensional
vector space. A characterization is given of it. This characterization makes
this order an order verifying the Jordan-Dedekind chain condition. We give
also a property for certain finite families of this order. More precisely, the
family of parts intervening in the linear representation of diagonalizable
endomorphism, that is, the orthogonal families forming a decomposition of
the identity endomorphism. |
| format | Article |
| id | doaj-art-11b0c366b9c842c0adb284824fa53e6c |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-11b0c366b9c842c0adb284824fa53e6c2025-08-20T02:01:53ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/783041783041Ordered Structures and ProjectionsM. Yazi0Probability and Statistics Department, Faculty of Mathematics, University of Sciences and Technology USTHB, 16111 Algiers, AlgeriaWe associate a covering relation to the usual order relation defined in the set of all idempotent endomorphisms (projections) of a finite-dimensional vector space. A characterization is given of it. This characterization makes this order an order verifying the Jordan-Dedekind chain condition. We give also a property for certain finite families of this order. More precisely, the family of parts intervening in the linear representation of diagonalizable endomorphism, that is, the orthogonal families forming a decomposition of the identity endomorphism.http://dx.doi.org/10.1155/2008/783041 |
| spellingShingle | M. Yazi Ordered Structures and Projections International Journal of Mathematics and Mathematical Sciences |
| title | Ordered Structures and Projections |
| title_full | Ordered Structures and Projections |
| title_fullStr | Ordered Structures and Projections |
| title_full_unstemmed | Ordered Structures and Projections |
| title_short | Ordered Structures and Projections |
| title_sort | ordered structures and projections |
| url | http://dx.doi.org/10.1155/2008/783041 |
| work_keys_str_mv | AT myazi orderedstructuresandprojections |