Vector properties of geometric calculus

Kaya Nurkan S., GÜRGİL İ., Kemal Karacan M.

Mathematical Methods in the Applied Sciences, vol.46, no.17, pp.17672-17691, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 17
  • Publication Date: 2023
  • Doi Number: 10.1002/mma.9525
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.17672-17691
  • Keywords: geometric inner product, geometric space, geometric vector product, multiplicative calculus
  • Uşak University Affiliated: Yes

Abstract

After its introduction by Grossman and Katz, the geometry part of geometric calculus has been mostly left unattended. In this paper, we give the elementary theorems to build the geometry on geometric space. We apply the well-known theorems for inner product in geometric space. The terms geometric determinant and geometric vector product are introduced, and their properties are studied. We give the definitions of the circle, the plane, and the sphere and visualize them along with a line in geometric space. Finally, we discuss the Gram–Schmidt process in geometric space.