Jordan Decomposition

A procedure that expresses a linear endomorphism of a finite-dimensional vector space (over a suitable field) as a direct sum of Jordan blocks, or equivalently decomposes an endomorphism into the commuting sum of a semisimple (diagonalisable) part and a nilpotent part that share the same generalized eigenspaces.

The canonical splitting of a linear endomorphism into a sum of commuting parts: a semisimple (diagonalizable) part and a nilpotent part, each a polynomial in the original operator; the decomposition is unique when it exists.