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Jadczyk, Arkadiusz; Szulga, Jerzy

Lorentz transformation from an elementary point of view. (English) Zbl 1356.15019

Electron. J. Linear Algebra 31, 794-833 (2016).
Summary: Elementary methods are used to examine some nontrivial mathematical issues underpinning the Lorentz transformation. Its eigen-system is characterized through the exponential of a G-skew symmetric matrix, underlining its unconnectedness at one of its extremes (the hypersingular case). A different yet equivalent angle is presented through Pauli coding which reveals the connection between the hypersingular case and the shear map.

Cited in 1 Document

MSC:

15B57 Hermitian, skew-Hermitian, and related matrices
17B81 Applications of Lie (super)algebras to physics, etc.
22E70 Applications of Lie groups to the sciences; explicit representations
15A18 Eigenvalues, singular values, and eigenvectors
15A16 Matrix exponential and similar functions of matrices

Keywords:

generalized Euler-Rodrigues formula; Minkowski space; Lorentz group; \(\mathrm{SL}(2,\mathbb C)\); \(\mathrm{SO}_0(3, 1)\); Lorentz transformation; eigensystem; exponential; skew symmetric matrix; hypersingular case; Pauli coding
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\textit{A. Jadczyk} and \textit{J. Szulga}, Electron. J. Linear Algebra 31, 794--833 (2016; Zbl 1356.15019)
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References:

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