Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 50, No. 1, pp. 215-218 (2009)

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Preservers of the rank of matrices over a field

Jozef Kalinowski

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

Abstract: In 2001, Li and Pierce characterized the linear operators that preserve the g rank of real matrices. The present paper describes all rank preserving maps $F: M_{m,n}(K) \longrightarrow M_{m,n}(K)$ of the $m\times n$ matrices over an arbitrary field $K$ which are of the form $F(a_{i,j})=(f_{i,j}(a_{i,j}))$. The linearity of $F$ is not a priorily assumed, and it turns out that if $\min \{m,n\}\leq 2$, then nonlinear rank preserving maps indeed exist.

Keywords: preservers; rank of matrices

Classification (MSC2000): 15A03

Full text of the article:

Electronic version published on: 29 Dec 2008. This page was last modified: 28 Jan 2013.

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