On calculation of spin group elements

We present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results using the Clifford algebra formalism in the case of arbitrary dimension and signature, and then in some special cases explicitly using matrices, quaternions, and split-quaternions. The different formalisms are convenient for different possible applications in physics, engineering, and computer science.
The work is supported by the project “Mirror Laboratories” of HSE University and North-Eastern Federal University “Quaternions, geometric algebras and applications”.