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%Fo�ner
%Ajda","ajda.fosner@uni-mb.si","
\section{Commutativity preserving maps on real matrices} By {\sl Ajda Fo\v sner}.  

\medskip  \noindent Let $M_n({\mathbb R})$ be the algebra of all $n\times n$ real matrices. A map $\phi : M_n({\mathbb R}) \to M_n({\mathbb R})$ preserves commutativity if $\phi (A) \phi (B) = \phi (B) \phi (A)$ whenever $AB = BA$, $A,B \in M_n({\mathbb R})$. If $\phi$ is bijective and both $\phi$ and $\phi^{-1}$ preserve commutativity, then we say that $\phi$ preserves commutativity in both directions. We will talk about non-linear maps on $M_n({\mathbb R})$ that preserve commutativity in both directions or in one direction only.
%commutativity preserving map, real Jordan canonical form","15A27","15A21","","07:49:06","Sun Mar 30 2008","86.58.80.16"
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