Resumen de On the convergence of generalized polar decompositions in Lie groups

Jordi P. García Seguí, Fernando Casas Pérez

• 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.