Editing Unimodular matrix (section)

{{about|matrices whose entries are [[integer number]]s|use of term '''unimodular''' in connection with [[polynomial matrix|polynomial matrices]]|Unimodular polynomial matrix}}
{{Use American English|date = January 2019}}
{{Short description|Integer matrices with +1 or -1 determinant; invertible over the integers. GL_n(Z)}}

In [[mathematics]], a '''unimodular matrix''' ''M'' is a [[square matrix|square]] [[integer matrix]] having [[determinant]] +1 or −1. Equivalently, it is an integer matrix that is [[invertible matrix|invertible]] over the [[integer]]s: there is an integer matrix ''N'' that is its inverse (these are equivalent under [[Cramer's rule]]). Thus every equation {{nowrap|1=''Mx'' = ''b''}}, where ''M'' and ''b'' both have integer components and ''M'' is unimodular, has an integer solution. The ''n''&thinsp;×&thinsp;''n'' unimodular matrices form a [[group (mathematics)|group]] called the ''n''&thinsp;×&thinsp;''n'' [[general linear group]] over <math>\mathbb{Z}</math>, which is denoted <math>\operatorname{GL}_n(\mathbb{Z})</math>.