Unimodularity

The word unimodularity describes various properties in mathematics :

• A unimodular affinity has determinants . ${\displaystyle \pm 1}$
• A unimodular form is a bilinear form whose associated matrix is ​​unimodular.
• A unimodular grid is a grid with discriminants . ${\displaystyle \pm 1}$
• A unimodular group is a locally compact topological group whose left and right hair measurements coincide.
• A unimodular complex number has magnitude , a unimodular function has complex values ​​of magnitude . ${\displaystyle 1}$ ${\displaystyle 1}$
• Depending on the definition, a matrix is ​​called unimodular if:
  • Its determinant is 1, so it is an element of the special linear group .
  • Its entries are integers and their determinant is 1 or −1, see integer unimodular matrix .
  • Its determinant is 1 or −1, see unimodular transformation .
  • The determinant is a unit (for matrices over a general commutative ring with one), i.e. the matrix is regular .

• A unimodular transformation is a linear transformation with whole rational coefficients and determinants . ${\displaystyle \pm 1}$
• A (finite-dimensional) Hopf algebra is unimodular if and only if every left integral is also a right one.