ON THE ROTATION MATRIX IN MINKOWSKI SPACE-TIME


ÖZDEMİR M., Erdogdu M.

REPORTS ON MATHEMATICAL PHYSICS, vol.74, no.1, pp.27-38, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 74 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.1016/s0034-4877(14)60055-0
  • Journal Name: REPORTS ON MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.27-38
  • Keywords: Minkowski space-time, rotation matrix, Rodrigues formula, QUATERNIONS
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, a Rodrigues-like formula is derived for 4 x 4 semi skew-symmetric real matrices in E-1(4). For this purpose, we use the decomposition of a semi skew-symmetric matrix A = theta(1)A(1) + theta(2)A(2) by two unique semi skew-symmetric matrices A(1) and A(2) satisfying the properties A(1)A(2) = theta, A(1)(3) = A1 and A(2)(3) = A(2). Then, we find Lorentzian rotation matrices with semi skew-symmetric matrices by Rodrigues-like formula. Furthermore, we give a way to find the semi skew-symmetric matrix A for a given Lorentzian rotation matrix R such that R = e(A).