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An element $u$ of a ring is unipotent when $u-1$ is nilpotent. For a matrix, this says that every eigenvalue is one. A unipotent algebraic group consists of unipotent elements in a faithful linear representation.

A unipotent algebraic group is built from unipotent elements. A unipotent algebraic group is an affine algebraic group all of whose elements are unipotent. The Kolchin theorem embeds it into an upper unitriangular group.