Geodesic
Additive rank-one nonincreasing maps on Hermitian matrices over the field $GF(2^2)$
The electronic journal of linear algebra, Tome 18 (2009), pp. 482-499.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A complete classification of additive rank-one nonincreasing maps on hermitian matrices over Galois field GF (2 2 ) is obtained. This field is special and was not covered in a previous paper. As a consequence, some known applications, like the classification of additive rank-additivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieties is also presented.
Classification : 15A04, 15A03, 15A57, 15A33, 05C12
Keywords: Hermitian matrix, rank, additive preserver, Galois field, weak homomorphism of a graph 
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     author = {Orel, Marko and Kuzma, Bojan},
     title = {Additive rank-one nonincreasing maps on {Hermitian} matrices over the field $GF(2^2)$},
     journal = {The electronic journal of linear algebra},
     pages = {482--499},
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     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/ELA_2009__18__a20/}
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Orel, Marko; Kuzma, Bojan. Additive rank-one nonincreasing maps on Hermitian matrices over the field $GF(2^2)$. The electronic journal of linear algebra, Tome 18 (2009), pp. 482-499. http://geodesic.mathdoc.fr/item/ELA_2009__18__a20/