2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69423Although there are many simple proofs of Jordan's decomposition theorem in the literature (see [1], the references mentioned there, and [2]), our proof seems to be even more elementary. In fact, all we need is the theorem on the dimensions of rang and kernel and the existence of eigenvalues of a linear transformation on a nontrivial finite dimensional complex vector space.2 pages, 3 added referencesHistory and Overview15A21text