Ordered Structures and Projections

Abstract EN

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.