# Unipotent matrix

From Encyclopedia of Mathematics

A square matrix over a ring for which the matrix , where is the order of , is nilpotent, i.e. . A matrix over a field is unipotent if and only if its characteristic polynomial is .

A matrix group is called unipotent if every matrix in it is unipotent. Any unipotent subgroup of , where is a field, is conjugate in to some subgroup of a special triangular group (Kolchin's theorem). This assertion is also true for unipotent groups over a skew-field, if the characteristic of the latter is either 0 or greater than some .

**How to Cite This Entry:**

Unipotent matrix. D.A. Suprunenko (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Unipotent_matrix&oldid=15993

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098