2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146409If F is an automorphism of the spectral unit ball, we show that, in a neighborhood of any cyclic (i.e. non-derogatory) matrix of the ball, the map F can be written as conjugation by a holomorphically varying non singular matrix. This provides a shorter proof of a theorem of J. Rostand, with a slightly stronger result.4 pagesComplex VariablesFunctional Analysis32H02 (Primary); 32A07, 15A21 (Secondary)text