Ordered Structures and Projections

M. Yazi

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-6

Abstract:

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.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:783041

DOI: 10.1155/2008/783041

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