Unimodular Transformation

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


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


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.

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