Structure of a linear endomorphism

Abstract

Given 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 eigenvalues