abs_vol18_pp482-499. 29KB Jun 04 2011 12:05:47 AM

ELA

ADDITIVE RANK–ONE NONINCREASING MAPS ON HERMITIAN

MATRICES OVER THE FIELD

GF

₍₂

2

₎

∗

MARKO OREL† _{AND BOJAN KUZMA}† ‡

Abstract. A complete classification of additive rank–one nonincreasing maps on hermitian ma-trices over Galois fieldGF₍₂2_{) 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 her-mitian varieties is also presented.

Key words. Hermitian matrix, Rank, Additive preserver, Galois field, Weak homomorphism of a graph.

AMS subject classifications.15A04, 15A03, 15A57, 15A33, 05C12.

∗_{Received by the editors February 28, 2009. Accepted for publication August 3, 2009. Handling}

Editor: Harm Bart. This work was supported by grants from the Ministry of Higher Education, Science and Technology, Slovenia.

†_{IMFM, Jadranska 19, 1000 Ljubljana, Slovenia (marko.orel@fmf.uni-lj.si).}

‡_{University of Primorska, Glagoljaˇska 8, 6000 Koper, Slovenia (bojan.kuzma@pef.upr.si).}

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 18, pp. 482-499, August 2009