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.