Jordan–Chevalley Decomposition

In mathematics, the Jordan–Chevalley decomposition, named after Camille Jordan and Claude Chevalley (also known as Dunford decomposition, named after Nelson Dunford, as well as SN decomposition), expresses a linear operator as the sum of its commuting semisimple part and its nilpotent parts. The multiplicative decomposition expresses an invertible operator as the product of its commuting semisimple and unipotent parts. The decomposition is important in the study of algebraic groups. The decomposition is easy to describe when the Jordan normal form of the operator is given, but it exists under weaker hypotheses than the existence of a Jordan normal form.

Read more about Jordan–Chevalley Decomposition:  Linear Operators, Banach Spaces