%0 Journal Article %T Hyper vector spaces over Krasner hyperfields %J Journal of Algebraic Hyperstructures and Logical Algebras %I University of Hatef (Hatef College University) %Z 2676-6000 %A Al-Tahan, M. %A Davvaz, B. %D 2020 %\ 08/01/2020 %V 1 %N 3 %P 61-72 %! Hyper vector spaces over Krasner hyperfields %K Krasner hyperfield %K hyper vector space %K subhyperspace %K linearly independent %K basis %K linear transformation %R 10.29252/hatef.jahla.1.3.5 %X In this paper, we study hyper vector spaces over Krasner hyperfields. First, we introduce the notions of linearly independence (dependence) and basis for a hyper vector space. Second, we investigate their properties and prove some results for hyper vector spaces that are similar to that of vector spaces over fields. Then, we define linear transformations over hyper vector spaces and investigate their properties. Finally, we prove the dimension theorem for linear transformations. %U https://jahla.hatef.ac.ir/article_113366_284ecb4e5f42e74f8f524aba5ec6ea4b.pdf