# Lattice

### From Online Dictionary of Crystallography

##### Revision as of 16:00, 10 April 2017 by MassimoNespolo (talk | contribs) (→See also: 6th edition of ITA)

Revision as of 16:00, 10 April 2017 by MassimoNespolo (talk | contribs) (→See also: 6th edition of ITA)

Réseau(*Fr*); Gitter (*Ge*); Reticolo(*It*); 格子 (*Ja*).

A **lattice** in the vector space **V ^{n}** is the set of all integral linear combinations

**t**=

*u*

_{1}

**a**+

_{1}*u*

_{2}

**a**+ ... +

_{2}*u*

_{k}

**a**of a system (

_{k}**a**,

_{1}**a**, ... ,

_{2}**a**) of linearly independent vectors in

_{k}**V**.

^{n}If *k = n*, i.e. if the linearly independent system is a **basis** of **V ^{n}**, the lattice is often called a

**full lattice**. In crystallography, lattices are almost always full lattices, therefore the attribute "full" is usually suppressed.

## See also

- crystallographic basis
- Sections 1.3.2 and 3.1 of
*International Tables for Crystallography, Volume A*, 6^{th}edition