Unimodular transformation

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.