# Unimodular transformation

From Encyclopedia of Mathematics

A linear transformation of a finite-dimensional vector space whose matrix has determinant .

#### Comments

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.

**How to Cite This Entry:**

Unimodular transformation. O.A. Ivanova (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Unimodular_transformation&oldid=14765

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098