Algebraic structure and basics of analysis of n-dimensional quaternionic space

Abstract

In this study, we focused on n-dimensional quaternionic space $H^n$ . To create the module structure, first part is devoted to define a metric depending on the product order relation of $R^n$ . The set of $H^n$ has been rewritten with a different representation of n-vectors. Using this notation, formulations corresponding to the basic operations in $H^n$ are obtained. By adhering these representations, module structure of $H^n$ over the set of real ordered n-tuples is given. Afterwards, we gave limit, continuity and the derivative basics of quaternion valued functions of a real variable.

Keywords: Componentwise multiplication; Symplectic geometry; n-Dimensional quaternionic space.