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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |