Bases in Min-Plus Algebra

DOI

10.2991/assehr.k.211122.044How to use a DOI?

Keywords

Basis; Linearly independent; Weak basis

Abstract

In classical linear algebra, a basis is a vector set that generates all elements in the vector space and that vector set is a linear independence set. However, the definitions of the linear dependence and independence in min-plus algebra are little more complex given that the min-plus algebra is the linear algebra over the commutative idempotent semiring. The definition of the linear dependence (independence) is used in this paper is Gondran-Minoux linear dependence (independence). A finite set is Gondran-Minoux linearly dependent if the set can be divided into two sets that form a linear space with an intersection which is not a zero vector. We will define the concept of the bases in min-plus algebra. In this paper also defined the concept of a weak bases and will be shown that the linear dependence (independence) is not needed to form a weak basis. In the last part of the research result’s are proven that every basis in a semimodules in min-plus algebra is a weak basis.

Copyright

© 2021 The Authors. Published by Atlantis Press SARL.

Open Access

This is an open access article under the CC BY-NC license.

Download article (PDF)

TY  - CONF
AU  - Syahida Amalia Rosyada
AU  - Siswanto
AU  - Vika Yugi Kurniawan
PY  - 2021
DA  - 2021/11/23
TI  - Bases in Min-Plus Algebra
BT  - Proceedings of the International Conference of Mathematics and Mathematics Education (I-CMME 2021)
PB  - Atlantis Press
SP  - 313
EP  - 316
SN  - 2352-5398
UR  - https://doi.org/10.2991/assehr.k.211122.044
DO  - 10.2991/assehr.k.211122.044
ID  - Rosyada2021
ER  -