Bases in Min-Plus Algebra
Syahida Amalia Rosyada, Siswanto Siswanto, Vika Yugi Kurniawan · Advances in Social Science, Education and Humanities Research/Advances in social science, education and humanities research · 2021
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.