Editing Dual lattice (section)

{{Short description|Construction analogous to that of a dual vector space}}
{{for|duals of order-theoretic lattices|Duality (order theory) }}
{{Group theory sidebar |Discrete}}

In the theory of [[Lattice (group)|lattices]], the '''dual lattice''' is a construction analogous to that of a [[Dual space|dual vector space]]. In certain respects, the geometry of the dual lattice of a lattice <math display = "inline"> L </math> is the reciprocal of the geometry of <math display = "inline"> L </math>, a perspective which underlies many of its uses.

Dual lattices have many applications inside of lattice theory, theoretical computer science, cryptography and mathematics more broadly. For instance, it is used in the statement of the [[Poisson summation formula]], transference theorems provide connections between the geometry of a lattice and that of its dual, and many lattice algorithms exploit the dual lattice.

For an article with emphasis on the physics / chemistry applications, see [[Reciprocal lattice]]. This article focuses on the mathematical notion of a dual lattice.