On the Algebra of Interval Vectors
Authors : Yılmaz YILMAZ, Halise LEVENT, Hacer BOZKURT
Pages : 67-79
Doi:10.36753/mathenot.1117985
View : 40 | Download : 68
Publication Date : 2023-06-30
Article Type : Research Article
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.Keywords : Quasilinear space, Interval vectors, Inner product quasilinear space, Hilbert quasilinear space