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Glite Dictionary
🟢 Modulus is one 🔢 Determinant is one
unimodular

unimodular

9.9
A square matrix whose determinant is 1 or -1
  • adjective
  • /ˌjuːnɪˈmɒdʒʊlər/
  • Specialized
: unimodular
  • We can view the first part of processing equalities as finding a unimodular transformation matrix U such that H = M. U is the Hermite normal form of M.

Examples

  • The mathematician demonstrated how to derive a unimodular matrix that satisfied the equation for the transformation.

  • To solve the system of equations, we need to find a unimodular transformation that simplifies the matrix.

  • In linear algebra, a matrix is termed unimodular if its determinant equals one.

Surface Forms

unimodular positive

Morphology

unimodular = modular (semi-transparent) = uni + modular

Formed from the prefix 'uni-' ('one') + 'modular', but the specialized mathematical sense 'determinant of ±1' is not fully predictable from these parts for a general learner.

Etymology

The word unimodular starts with uni- meaning 'one', like unit, and ends with modulus meaning 'measure' or 'size'. So a unimodular matrix has a 'measure' of one — its determinant is plus or minus one, which is why it preserves volume.