The name "unimodular transformation" is often restricted to mean a linear transformation with determinant . In the context of a vector space over a field which is the quotient field of an integral domain , with a fixed -basis in , a linear transformation is called unimodular if its matrix with respect to has entries in and determinant a unit in . Under each of these definitions the unimodular transformations form a group. In the case of linear transformations with determinant one often calls this the unimodular group, or, more commonly nowadays, the special linear group.
Unimodular transformation. O.A. Ivanova (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Unimodular_transformation&oldid=14765