Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 2, pp. 519-526 (2006)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Rank of Matrices and the Pexider Equation

Józef Kalinowski

Uniwersytet \'Sl\c aski, Instytut Matematyki, ul. Bankowa 14, 40-007 Katowice, Poland; e-mail:

Abstract: 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:

Electronic version published on: 19 Jan 2007. This page was last modified: 5 Nov 2009.

© 2007 Heldermann Verlag
© 2007–2009 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition