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, cilt.24, sa.1, ss.179-192, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 1
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s00006-013-0424-2
  • Dergi Adı: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.179-192
  • Anahtar Kelimeler: Quaternions, Split Quaternions, Rotation Matrix
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.