Vale Gonsalves, María Jesús2022-08-262022-08-262022http://hdl.handle.net/10347/29149Given an n-dimensional vector space V over a field K, it is proved that if f is an endomorphism of V whose characteristic polynomial has its n roots in K, then f has a Jordan canonical form. The concept of nilpotent endomorphism is defined and the Jordan-Chevalley decomposition theorem is proved. From this theorem it is possible to calculate the powers and the exponential of complex matrices, knowing their eigenvalueseng©2022, A autora. Este traballo está baixo unha licenza Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/EigenvaluesEigenvectorsSimilar matricesJordan canonical form of an endomorphism and of a matrixNilpotenceJordan-Chevalley decompositionPowers of endomorphisms and matricesExponential matrixotheropen access