Maximal column ranks and their preservers of matrices over max algebra

Seok-Zun Song; Kyung-Tae Kang

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J. Korean Math. Soc. 2003; 40(6): 943-950

Printed November 1, 2003

Maximal column ranks and their preservers of matrices over max algebra

Seok-Zun Song and Kyung-Tae Kang

Cheju National University, Cheju National University

Abstract

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Abstract

The maximal column rank of an $m$ by $n$ matrix $A$ over max algebra is the maximal number of the columns of $A$ which are linearly independent. We compare the maximal column rank with rank of matrices over max algebra. We also characterize the linear operators which preserve the maximal column rank of matrices over max algebra.

Keywords: max algebra, rank, maximal column rank, monomial, linear operator

MSC numbers: Primary 15A03, 15A04