Formulas for the Matrix Cosine and Sine of the Lie Algebra of Lorentz Matrix Lie Group SO(1, 3)

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Published: Dec 27, 2023
Keywords:
Matrix cosine Matrix sine Sylvester’s formula Lie algebra of Lorentz matrix Lie group

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Poonchayar Patthanangkoor
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120
Koranan Kaewkumsai
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120
Nattawadee Charoenthong
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120
Siripatana Tikamma
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120

Abstract

In this paper the formulas of the matrix cosine of gif.latex?B and the matrix sine of gif.latex?B, where gif.latex?B is an element of gif.latex?so(1,3) which is the Lie algebra of Lorentz matrix Lie group, are derived.


 

Article Details

Issue
Vol.31 No.6 (November-December 2023)
Section
Physical Sciences

References

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Politi, T., 2001, A Formula for the Exponential of a Real Skew-Symmetric Matrix of Order 4, BIT, Numeric Analysis. 41: 842-845.