# Lattice

### From Online Dictionary of Crystallography

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}**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
- Chapters 1.3.2 and 3.1 of
*International Tables for Crystallography, Volume A*, 6th edition