On the Orthogonality in Real Symbolic 2-Plithogenic and 3-Plithogenic Vector Spaces

Abstract

This paper is dedicated to study the real inner product defined over symbolic 2-plithogenic vector spaces, where we discuss the concept of inner (scalar) products over the symbolic 2-plithogenic vector spaces by using the corresponding Euclidean scalar products to get theorems that describe the conditions of orthogonality in this class of spaces. Also, we give many examples to explain the ortho-normed symbolic 2-plithogenic spaces.

Keywords

• symbolic 2-plithogenic vector space
• inner product
• orthogonal basis
• ortho-normed basis