Generalized Euler-Rodrigues formula, Minkowski space, Lorentz group, SL(2, C), SO_0(3, 1)
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 hyper-singular case). A different yet equivalent angle is presented through Pauli coding which reveals the connection between the hyper-singular case and the shear map.
Jadczyk, Arkadiusz and Szulga, Jerzy.
"Lorentz transformation from an elementary point of view",
Electronic Journal of Linear Algebra,
Volume 31, pp. 794-833.