Ramakrishna, Viswanath2017-08-292017-08-292017-082017-08August 201http://hdl.handle.net/10735.1/5472The double covering of Orthogonal groups by the Spin groups is vital for many applications. In this dissertation, we address the important question of inverting the covering map φ_{p,q} : Spin⁺(p,q) → SO⁺(p,q) for (p,q)∈ (2,1),(2,2),(3,1),(3,2),(3,3) in the indefinite case. We also develop explicit formulae for the forward map φ_{p,q} : Spin⁺(p,q) → SO⁺(p,q) for (p,q)∈ (1,2),(1,3),(2,3). We do not work with the even subalgebra of Cl(p,q) and thus our formulae are quite explicit. Our method relies significantly on standard Givens and hyperbolic Givens.application/pdfenCopyright ©2017 is held by the author. Digital access to this material is made possible by the Eugene McDermott Library. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.Clifford algebrasGroup theoryDecomposition (Mathematics)Dissertation2017-08-29