Rank preservers of matrices over max algebra

Abstract

The max algebra consists of the nonnegative real numbers equipped with two binary operations, maximization and multiplication. We consider the semimodules over max algebra and study the properties of the weak basis and weak dimension of the semi-modules. Moreover, we obtain the characterizations of those linear operators that preserve rank of matrices over max-algebra.

Keywords:

• Max algebra
• Linear operator
• Rank preserver

AMS Subject Classification:

• 15A03
• 15A04

^∗e-mail: [email protected]

^†Corresponding author. This work was supported by Korea Research Foundation Grant (KRF-99-015-DI0003)

^∗e-mail: [email protected]

^†Corresponding author. This work was supported by Korea Research Foundation Grant (KRF-99-015-DI0003)

Notes

^∗e-mail: [email protected]

^†Corresponding author. This work was supported by Korea Research Foundation Grant (KRF-99-015-DI0003)