English

Quadratic Forms and their Number Systems and Geometry

General Mathematics 2022-04-12 v1

Abstract

Quaternions, split quaternions, and hybrid numbers are very well-known number systems. These number systems are used to make geometry in Euclidean and Lorentz spaces. These number systems can be obtained with the help of a quadratic form. This article examines how to find the corresponding number system for any quadratic form. As a result of this examination, bilinear form, vector product, skew-symmetric matrix, and rotation matrices corresponding to any number system were obtained.

Keywords

Cite

@article{arxiv.2204.05115,
  title  = {Quadratic Forms and their Number Systems and Geometry},
  author = {İskender Öztürk},
  journal= {arXiv preprint arXiv:2204.05115},
  year   = {2022}
}

Comments

19 pages, 0 figures

R2 v1 2026-06-24T10:44:30.934Z