International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 783041, 6 pages
doi:10.1155/2008/783041
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.