# Lattice

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

_{k}**a**,

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

_{2}**a**) of

_{k}**V**.

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

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

### See also

- Sections 8.1 and 9.1 of
*International Tables for Crystallography, Volume A*