Inversion of the Indefinite Double Covering Map

By : F. Adjei, M.K. Dabkowski, S. Khan, V. Ramakrishna

Page No: 233-281

Abstract: 
Algorithmic methods for the explicit inversion of the indefinite double covering maps are proposed. These are based on either the Givens decomposition or the polar decomposition of the given matrix in the proper, indefinite orthogonal group SO+(p, q). As a by-product we establish that the preimage in the covering group, of a positive matrix in SO+(p, q), can always be chosen to be itself positive definite. Inversion amounts to solving a polynomial system. These methods solve this system by either inspection, Grebner bases or by inverting the associated Lie algebra isomorphism and computing certain exponentials explicitly. The techniques are illustrated for (p, q) Î {(2,1), (2,2), (3,2), (4,1)}.

Authors :
F. Adjei
Department of Mathematics, Prairie View A&M University, Prairie View, TX 77446, USA.

M.K. Dabkowski
Department of Mathematical Sciences, The University of Texas at Dallas, Richardson TX, 75080, USA.

S. Khan
Department of Mathematical Sciences, The University of Texas at Dallas, Richardson TX, 75080, USA.

V. Ramakrishna
Department of Mathematical Sciences, The University of Texas at Dallas, Richardson TX, 75080, USA.
 

DOI: https://doi.org/10.32381/JCISS.2020.45.1-4.6