Unipotent

Unipotent

In mathematics, a unipotent element r of a ring R is one such that r − 1 is a nilpotent element, in other words such that some power (r − 1)n is zero.

In particular a square matrix M is a unipotent matrix if and only if its characteristic polynomial P(t) is a power of t − 1. Equivalently, M is unipotent if all its eigenvalues are 1.

The term quasi-unipotent means that some power is unipotent, for example for a diagonalizable matrix with eigenvalues that are all roots of unity.

A unipotent affine algebraic group is one all of whose elements are unipotent (see below for the definition of an element being unipotent in such a group).