Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 47, No. 2, pp. 519526 (2006) 

Rank of Matrices and the Pexider EquationJózef KalinowskiUniwersytet \'Sl\c aski, Instytut Matematyki, ul. Bankowa 14, 40007 Katowice, Poland; email: 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, ChiKwong; Pierce, S.: Linear Preserver Problems. Amer. Math. Monthly {\bf 108} (2001), 591605. Keywords: rank of matrices Classification (MSC2000): 15A03 Full text of the article:
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