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A [[Linear transformation|linear transformation]] of a finite-dimensional [[Vector space|vector space]] whose matrix has determinant  $  \pm  1 $.

====Comments====
The name  "unimodular transformation"  is often restricted to mean a linear transformation with determinant  $  1 $. 
In the context of a vector space  $  V $
over a field  $  k $
which is the quotient field of an integral domain  $  D $, 
with a fixed  $  k $-
basis  $  a _ {1} \dots a _ {n} $
in  $  V $, 
a linear transformation is called unimodular if its matrix with respect to  $  a _ {1} \dots a _ {n} $
has entries in  $  D $
and determinant a unit in  $  D $. 
Under each of these definitions the unimodular transformations form a group. In the case of linear transformations with determinant  $  1 $
one often calls this the [[Unimodular group|unimodular group]], or, more commonly nowadays, the [[Special linear group|special linear group]].