Home Page

Author Index

Reviewer Index

Editorial Index

 
     JJMS Home Page
 
 Jordanian Journals  
Home  

Editorial Board

 
  - Editors  
  - Associate Editorial Board  
Advisory Board  
Forthcoming Papers
Latest Issue

Back Issues

Publication Ethics

Manuscript Organization  
Electronic Submission  

Electronic Online Submission

Contact Address  
Arabic WebSite  
 

 

 

Characterization of Rank of a Matrix Over the Symmetrized Max-Plus Algebra

Suroto (1), Diah Junia Eksi Palupi (2) and Ari Suparwanto (3)

(1) Department of Mathematics, Universitas Jenderal Soedirman, Purwokerto,
Central Java, Indonesia

Email address: suroto@unsoed.ac.id

 

(2) Department of Mathematics, Universitas Gadjah Mada, Yogyakarta, Indonesia

Email address: diah yunia@ugm.ac.id

 

(3) Department of Mathematics, Universitas Gadjah Mada, Yogyakarta, Indonesia

Email address: ari_suparwanto@ugm.ac.id

Doi : https://doi.org/10.47013/15.4.4

Cited by : Jordan J. Math & Stat., 15 (4A) (2022), 843 - 856

PDF

Received on: April 16, 2021;                                           Accepted on: Feb. 27, 2022

 Abstract. In this paper, we characterize the rank of a matrix over the symmetrized max-plus algebra. This characterization is based on linearly independence of columns or rows of the matrix in balance sense. We show that the rank of such a matrix can be determined using maximum number of rows or columns which are linearly independent in balance sense. This completes the discussion in [1] which only uses minors to determine rank of matrix.

Keywords: Characterization, Rank, Linear Independent, Symmetrized Max-Plus Algebra.