A unimodular transformation is a transformation 
for which the determinant
of the matrix 
satisfies
 |
A necessary and sufficient condition that a linear transformation map a point lattice onto itself is that its matrix in a lattice vector basis have integer entries and be unimodular.
If 
is a complex number, then the transformation
 |
is called unimodular if 
, 
, 
, and 
are integers with 
. The set of all unimodular transformations forms the
modular group Gamma.
