@misc{Bajorska_Beata_On, author={Bajorska, Beata}, howpublished={online}, language={eng}, abstract={Expressing a linear operator on a finite dimensional vector space over any field K as a sum of two commuting operators - semisimple and nilpotent - is called the Jordan-Chevalley decomposition of f. It is known that this decomposition exists for an arbitrary f if only K is perfect. In this paper we give some methods for determining the decomposition. }, title={On Jordan-Chevalley decomposition}, keywords={linear operator, Jordan-Chevalley decomposition, perfect field}, }