Bases in Min-Plus Algebra
- 10.2991/assehr.k.211122.044How to use a DOI?
- Basis; Linearly independent; Weak basis
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.
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Cite this article
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 -