What is "unipotent"

a. 1 (context biology English) Having the capacity to develop into only one type of cell or tissue 2 (context mathematics English) Having a single idempotent element

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

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.

In an unipotent affine algebraic group, all elements are unipotent (see below for the definition of an element being unipotent in such a group).