Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:basisFor |
n linearly independent vectors in R^n
|
| gptkbp:definedIn |
discrete subgroup of R^n
set of all integer linear combinations of n linearly independent vectors in R^n |
| gptkbp:dimensions |
n
|
| gptkbp:example |
gptkb:Weyl_group
gptkb:E8_lattice gptkb:Leech_lattice Z^n |
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:hasProperty |
discrete
periodic locally compact free abelian group additive group determinant is the volume of the fundamental parallelepiped basis is not unique can be represented by a matrix of basis vectors can be transformed by unimodular matrices closed under addition and subtraction contains the zero vector finite covolume invariant under translation by lattice vectors isomorphic to Z^n as a group no accumulation points except at infinity periodic tiling of R^n rank n spans R^n all points are integer combinations of basis vectors |
| gptkbp:hasSubfield |
gptkb:algebra
gptkb:geometry number theory |
| https://www.w3.org/2000/01/rdf-schema#label |
lattice in R^n
|
| gptkbp:rank |
n
|
| gptkbp:relatedTo |
gptkb:Gram_matrix
gptkb:Minkowski's_theorem gptkb:integer_lattice gptkb:Voronoi_cell Bravais lattice fundamental domain lattice basis reduction shortest vector problem closest vector problem determinant of a lattice |
| gptkbp:used_in |
coding theory
cryptography crystallography optimization sphere packing |
| gptkbp:bfsParent |
gptkb:torus_group
|
| gptkbp:bfsLayer |
5
|