Ordered Structures and Projections
2008 ◽
Vol 2008
◽
pp. 1-6
Keyword(s):
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.
1982 ◽
Vol 25
(2)
◽
pp. 133-139
◽
1995 ◽
Vol 138
◽
pp. 113-140
◽
1986 ◽
Vol 69
(4)
◽
pp. 37-46
◽
2009 ◽
Vol 20
(11)
◽
pp. 1347-1362
◽