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Unimodular Transformation


A transformation x^'=Ax is unimodular if the determinant of the matrix A satisfies

 det(A)=+/-1.

A necessary and sufficient condition that a linear transformation transform a lattice to itself is that the transformation be unimodular.

If z is a complex number, then the transformation

 z^'=(az+b)/(cz+d)

is called a unimodular if a, b, c, and d are integers with ad-bc=1. The set of all unimodular transformations forms a group called the modular group.


See also

Modular Group Gamma, Modular Group Lambda

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Cite this as:

Weisstein, Eric W. "Unimodular Transformation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UnimodularTransformation.html

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