# Lattice

(Difference between revisions)
 Revision as of 14:35, 15 May 2017 (view source)m (Style edits to align with printed edition)← Older edit Revision as of 09:21, 12 October 2017 (view source)m (languages)Newer edit → Line 1: Line 1: - Réseau(''Fr''). Gitter (''Ge''). Reticolo(''It''). 格子 (''Ja''). + مشبك (''Ar''); Réseau (''Fr''); Gitter (''Ge''); Reticolo (''It''); 格子 (''Ja''); Решётка (''Ru''); Red (''Sp''). + A '''lattice''' in the vector space '''V'''''n'' is the set of all integral linear combinations '''t''' = ''u''1'''a1''' + ''u''2'''a2''' + ... + ''u''k'''ak''' of a system ('''a1''', '''a2''', ... , '''ak''') of linearly independent vectors in '''V'''''n''. A '''lattice''' in the vector space '''V'''''n'' is the set of all integral linear combinations '''t''' = ''u''1'''a1''' + ''u''2'''a2''' + ... + ''u''k'''ak''' of a system ('''a1''', '''a2''', ... , '''ak''') of linearly independent vectors in '''V'''''n''.

## Revision as of 09:21, 12 October 2017

مشبك (Ar); Réseau (Fr); Gitter (Ge); Reticolo (It); 格子 (Ja); Решётка (Ru); Red (Sp).

A lattice in the vector space Vn is the set of all integral linear combinations t = u1a1 + u2a2 + ... + ukak of a system (a1, a2, ... , ak) of linearly independent vectors in Vn.

If k = n, i.e. if the linearly independent system is a basis of Vn, the lattice is often called a full lattice. In crystallography, lattices are almost always full lattices, therefore the attribute 'full' is usually suppressed.