2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168987We study first order differential operators with constant coefficients. The main question is under what conditions a generalized Poincaré inequality holds. We show that the constant rank condition is sufficient. The concept of the Moore-Penrose generalized inverse of a matrix comes into play.8 pages, 0 figures submitted to Proceedings of the American Mathematical Society. Problem with bibliography correctedAnalysis of PDEsClassical Analysis and ODEs35J45 (Primary) 35B45, 58J10 (Secondary)text