Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 2, pp. 435446 (2004) 

Adjacency preserving mappings of rectangular matricesWenling Huang and ZheXian WanFachbereich Mathematik, Schwerpunkt GD, Universit{ä}t Hamburg, Bundesstr. 55, 20146 Hamburg, Germany, email: huang@math.unihamburg.de; Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080 Beijing, and Center for Combinatorics, Nankai University, 300071 Tienjin, China email: wan@it.lth.seAbstract: Let $D$ be a division ring and let $m,n$ be integers $\ge 2$. Let $M_{m\times n}(D)$ be the space of $m\times n$ matrices. In the fundamental theorem of the geometry of rectangular matrices all bijective mappings $\vp$ of $M_{m\times n}(D)$ are determined such that both $\varphi$ and ${\varphi}^{1}$ preserve adjacency. We show that if a bijective map $\varphi$ of $M_{m\times n}(D)$ preserves the adjacency then also ${\varphi}^{1}$ preserves the adjacency. Thus the supposition that ${\varphi}p^{1}$ preserves adjacency may be omitted in the fundamental theorem. Keywords: Geometry of matrices, rectangular matrices, mappings preserving adjacency, distance preserving mappings Classification (MSC2000): 15A99, 51D20 Full text of the article:
Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.
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