Geodesic
Idempotence-preserving maps between matrix spaces over fields of characteristic 2
The electronic journal of linear algebra, Tome 21 (2010), pp. 110-123.

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

Summary: Let M n (F) be the space of all n $\times n$ matrices over a field F of characteristic 2 other than F $2 = {0, 1}$, and let P n (F) be the subset of M n (F) consisting of all n $\times n$ idempotent matrices. Let m and n be integers with n $\geq m$ and n $\geq 3$. We denote by $\Phi n$,m (F) the set of all maps from Mn (F) to M m (F) satisfying that A - $\lambda B \in P$ n (F) implies $\varphi (A) - \lambda \varphi (B) \in P$ m (F) for all A, B $\in M$ n (F) and $\lambda \in F$. In this paper, we give a complete characterization of $\Phi n$,m (F).
Classification : 15A04
Keywords: field, characteristic, idempotence, preserving, homogeneous 
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     title = {Idempotence-preserving maps between matrix spaces over fields of characteristic 2},
     journal = {The electronic journal of linear algebra},
     pages = {110--123},
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     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/ELA_2010__21__a3/}
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Xu, Jin-Li; Tang, Xiao-Min; Cao, Chong-Guang. Idempotence-preserving maps between matrix spaces over fields of characteristic 2. The electronic journal of linear algebra, Tome 21 (2010), pp. 110-123. http://geodesic.mathdoc.fr/item/ELA_2010__21__a3/