On the Eigenvalues and Eigenvectors of a Lorentzian Rotation Matrix by Using Split Quaternions
Küçük Resim Yok
Tarih
2014
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Basel Ag
Erişim Hakkı
info:eu-repo/semantics/closedAccess
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.
Açıklama
Anahtar Kelimeler
Quaternions, Split Quaternions, Rotation Matrix
Kaynak
Advances In Applied Clifford Algebras
WoS Q Değeri
Q3
Scopus Q Değeri
Q3
Cilt
24
Sayı
1
