Cayley formula in Minkowski space-time

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Atıf İçin Kopyala

Erdogdu M., ÖZDEMİR M.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, cilt.12, sa.5, 2015 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 12 Sayı: 5
• Basım Tarihi: 2015
• Doi Numarası: 10.1142/s0219887815500589
• Dergi Adı: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Anahtar Kelimeler: Minkowski space-time, rotation matrix, Cayley formula, ROTATION MATRIX
• Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, Cayley 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) = 0, A(1)(3) = A(1) and A(2)(3) = -A(2). Then, we find Lorentzian rotation matrices with semi-skew-symmetric matrices by Cayley formula. Furthermore, we give a way to find the semi-skew-symmetric matrix A for a given Lorentzian rotation matrix R such that R = Cay(A).