Lattice

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

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 of Crystallography, Volume A

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