Lattice

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

Definition

A lattice in the vector space Vⁿ is the set of all integral linear combinations t = u₁a₁ + u₂a₂ + ... + u_ka_k of a system (a₁, a₂, ... , a_k) 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.

See also

• crystallographic basis
  
• Sections 8.1 and 9.1 of International Tables for Crystallography, Volume A

---