Unimodular matrix

Summary

A unimodular matrix is a square matrix with integer entries and determinant $+1$ or $-1$. These are exactly the integer matrices whose inverse also has integer entries. They form the group $\mathrm{GL}_n(\Z)$, the general linear group over the integers. Unimodular matrices describe the changes of basis of the lattice $\Z^n$, and they appear in the Smith and Hermite normal forms.