On the Algebra of Interval Vectors

Authors : Yılmaz YILMAZ, Halise LEVENT, Hacer BOZKURT

Pages : 67-79

Doi:10.36753/mathenot.1117985

View : 71 | Download : 77

Publication Date : 2023-06-30

Article Type : Research Paper

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 $insert ignore into journalissuearticles values(n_{r},n_{s});$-dimensional quasilinear space and any quasilinear space is $\\leftinsert ignore into journalissuearticles values( n_{r},0_{s}\\right); $-dimensional if and only if it is $n$-dimensional linear space. We also give examples of $insert ignore into journalissuearticles values(2_{r},0_{s});$ and $insert ignore into journalissuearticles values(0_{r},2_{s});$-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

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