On the Eigenvalues and Eigenvectors of a Lorentzian Rotation Matrix by Using Split Quaternions

ÖZDEMİR M., Erdogdu M., Şimşek H.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.24, no.1, pp.179-192, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.1007/s00006-013-0424-2
  • Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.179-192
  • Keywords: Quaternions, Split Quaternions, Rotation Matrix
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, we examine eigenvalue problem of a rotation matrix in Minkowski 3 space by using split quaternions. We express the eigenvalues and the eigenvectors of a rotation matrix in term of the coefficients of the corresponding unit timelike split quaternion. We give the characterizations of eigenvalues (complex or real) of a rotation matrix in Minkowski 3 space according to only first component of the corresponding quaternion. Moreover, we find that the casual characters of rotation axis depend only on first component of the corresponding quaternion. Finally, we give the way to generate an orthogonal basis for by using eigenvectors of a rotation matrix.