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Ordered Structures and Projections

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  • M. Yazi

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.

Suggested Citation

  • M. Yazi, 2008. "Ordered Structures and Projections," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-6, April.
    • Handle: RePEc:hin:jijmms:783041
    DOI: 10.1155/2008/783041
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