Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 47, No. 2, pp. 519-526 (2006)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 47, No. 2, pp. 519-526 (2006) |
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Rank of Matrices and the Pexider EquationJózef KalinowskiUniwersytet \'Sl\c aski, Instytut Matematyki, ul. Bankowa 14, 40-007 Katowice, Poland; e-mail: kalinows@ux2.math.us.edu.plAbstract: The paper [L] gives a characterization of those linear operators which preserve the rank of matrices over $\R$. In this paper we characterize the operators of type (1) having this property, without making the linearity assumption. For matrices from $M_{n,m}$ and $\min\{n,m\}\geq3$ the operator must be linear and of the form from [L]. If $1\leq\min\{n,m\}\leq 2$, then the operator may be nonlinear. [L] Li, Chi-Kwong; Pierce, S.: Linear Preserver Problems. Amer. Math. Monthly {\bf 108} (2001), 591--605. Keywords: rank of matrices Classification (MSC2000): 15A03 Full text of the article (for subscribers):
Electronic version published on: 19 Jan 2007. This page was last modified: 6 Jul 2007.
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