GEOMETRIC APPROACHES TO ESTABLISH THE FUNDAMENTALS OF LORENTZ SPACES (Formula Presented) AND (Formula Presented)

Çoruh Şenocak S., Yüce Samsun S.

Mathematica Bohemica, vol.149, no.4, pp.549-567, 2024 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 149 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.21136/mb.2024.0111-23
  • Journal Name: Mathematica Bohemica
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.549-567
  • Keywords: Gram-Schmidt method, hyperbolic cosine formulas, Lorentz matrix multiplication, Lorentz triangle, orthogonal projection, Pedoe inequality
  • Yıldız Technical University Affiliated: Yes

Abstract

The aim of this paper is to investigate the orthogonality of vectors to each other and the Gram-Schmidt method in the Minkowski space (Formula Presented). Hyperbolic cosine for mulas are given for all triangle types in the Minkowski plane (Formula Presented). Moreover, the Pedoe inequality is explained for each type of triangle with the help of hyperbolic cosine formulas. Thus, the Pedoe inequality allowed us to establish a connection between two similar triangles in the Minkowski plane. In the continuation of the study, the rotation matrix that provides both point and axis rotation in the Minkowski plane is obtained by using the Lorentz matrix multiplication. Also, it is stated to be an orthogonal matrix. Moreover, the orthogonal projection formulas on the spacelike and timelike lines are given in the Minkowski plane. In addition, the distances of any point from the spacelike or timelike line are formulated.