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Glite Dictionary
🟢 Modulus is one 🔢 Determinant is one
unimodular

unimodular

1 9.9
A complex number with absolute value equal to one
  • adjective
  • /ˌjuːnɪˈmɒdʒʊlər/
  • Specialized
: unimodular
  • A unimodular complex number lies exactly on the unit circle in the complex plane.

Examples

  • In complex analysis, a unimodular number always lies on the unit circle.

  • The transformation preserves length because it is defined by a unimodular operator.

  • In mathematics, a unimodular matrix has a determinant of one or negative one.

  • The matrix is unimodular because its determinant equals one.

  • A unimodular matrix is essential for preserving volume in transformations.

  • A unimodular matrix has a determinant of one, making it important in linear algebra.

  • To ensure stability, the transformation must be represented by a unimodular matrix.

Surface Forms

unimodular positive

Morphology

unimodular = modular (transparent) = uni + modular

The prefix 'uni-' ('one') combined with 'modular' (relating to modulus) directly suggests 'having modulus one', which matches this mathematical sense.

Etymology

The word unimodular combines uni- meaning 'one', like unit, and modulus meaning 'measure', so it literally means 'measure one'. That's why a unimodular complex number has absolute value one and lies on the unit circle, and a unimodular matrix has modulus one.