On the Algebra of Interval Vectors

Abstract

In this study, we examine some important subspaces by showing that the set of n-dimensional interval vectors is a quasilinear space. By defining the concept of dimensions in these spaces, we show that the set of $n$-dimensional interval vectors is actually a $(n_{r},n_{s})$-dimensional quasilinear space and any quasilinear space is $\left( n_{r},0_{s}\right) $-dimensional if and only if it is $n$-dimensional linear space. We also give examples of $(2_{r},0_{s})$ and $(0_{r},2_{s})$-dimensional subspaces. We define the concept of dimension in a quasilinear space with natural number pairs. Further, we define an inner product on some spaces and talk about them as inner product quasilinear spaces. Further, we show that some of them have Hilbert quasilinear space structure.