Unipotent

A square matrix is said to be unipotent if , where is an identity matrix is a nilpotent matrix (defined by the property that is the zero matrix for some positive integer matrix power ). The corresponding identity, for some integer allows this definition to be generalized to other types of algebraic systems.

An example of a unipotent matrix is a square matrix whose entries below the diagonal are zero and its entries on the diagonal are one. An explicit example of a unipotent matrix is given by

One feature of a unipotent matrix is that its matrix powers have entries which grow like a polynomial in .

A semisimple element of a group is unipotent if is a p-group, where is the generalized fitting subgroup.