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

In this study, we focused on n-dimensional quaternionic space [Formula: see text]. To create the module structure, first part is devoted to define a metric depending on the product order relation of [Formula: see text]. The set of [Formula: see text] has been rewritten with a different representation of n-vectors. Using this notation, formulations corresponding to the basic operations in [Formula: see text] are obtained. By adhering these representations, module structure of [Formula: see text] 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.