Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 45, No. 2, pp. 435-446 (2004)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 2, pp. 435-446 (2004) |
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Adjacency preserving mappings of rectangular matricesWen-ling Huang and Zhe-Xian WanFachbereich Mathematik, Schwerpunkt GD, Universit{ä}t Hamburg, Bundesstr. 55, 20146 Hamburg, Germany, e-mail: huang@math.uni-hamburg.de; Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080 Beijing, and Center for Combinatorics, Nankai University, 300071 Tienjin, China e-mail: 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.
© 2004 Heldermann Verlag
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