Linear Functionals on Hypervector Spaces

Abstract

We study main properties of linear functionals on hypervector spaces. In this way, we obtain the dual basis of a given basis of a finite-dimensional hypervector space. Moreover, we investigate the relation between linear functionals and subhyperspaces and conclude dim V*=dim V, dim (W_1+W_2)=dim W_1+dim W_2-dim (W_1\cap W_2) and dim W+dim W^\circ=dim V. Also, we show that every superhyperspace is the kernel of a linear functional. Finally, we check out whether every basis for V* is the dual of some basis for V.