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Unimodular transformation

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


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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