SOME RESULTS ON HYPERVECTOR SPACES

Abstract

The aim of this paper is to study hypervector spaces.  In this regard at first some new nontrivial examples of hypervector spaces are introduced.  Then the notions of linearly span, linearly independence, basis, ordered basis, coordinates and linear transformation are investigated and some related results are obtained.  Especially, it is proved that for a linear transformation T : V \(\longrightarrow\) W between two hypervector spaces, dim ker T + dim T(V) = dim V, and under certain conditions dim L(V,W) = dim V × dim W.