Unimodular matrix
Integer matrices with +1 or -1 determinant; invertible over the integers. GL_n(Z) / From Wikipedia, the free encyclopedia
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This article is about matrices whose entries are integer numbers. For use of term unimodular in connection with polynomial matrices, see Unimodular polynomial matrix.
In mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over the integers: there is an integer matrix N that is its inverse (these are equivalent under Cramer's rule). Thus every equation Mx = b, where M and b both have integer components and M is unimodular, has an integer solution. The n × n unimodular matrices form a group called the n × n general linear group over , which is denoted .