On the convergence of generalized polar decompositions in Lie groups

Autores: Jordi P. García Seguí, Fernando Casas Pérez
Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 33, 2010, págs. 113-124
Idioma: inglés
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Resumen
- We analyze the so-called generalized polar decomposition determined by an involutive automorphism in a Lie group. This concept generalizes the well known factorization of a matrix as the product of a positive semidefinite matrix and an orthogonal matrix in linear algebra. We provide a different constructive proof of the existence of such a decomposition in a neighborhood of the identity and obtain several explicit bounds on the convergence domain of the series defined each factor.