Jordan form of an endomorphism
We call -Jordan cell a matrix which has a particular form.
In 4-dimension we have
We say that an endomorphism is in Jordan form if there is a basis of the vector space in which the matrix associated to endomorphism is a "diagonal "matrix of Jordan cells.
Necessary and sufficient condition for an endomorphism to admit a Jordan form is that the characteristic polynomial has n solution (eigenvalues for endomorphism) in field k.