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lattice in the vector space Vn is the set of all integral linear combinations t = u1a1 + u2a2 + ... + ukak of a system (a1a2, ... , ak) 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

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