functional analysis, a normed lattice is a topological vector lattice that is also a normed space whose unit ball is a solid set. Normed lattices are important...

functional analysis and order theory, a Banach lattice (X,‖·‖) is a complete normed vector space with a lattice order, ≤ {\displaystyle \leq } , such that...

convex vector lattice Normed lattice Ordered vector space – Vector space with a partial order Pseudocomplement Riesz space – Partially ordered vector space...

of a lattice Fréchet lattice – Topological vector lattice Normed lattice Vector lattice – Partially ordered vector space, ordered as a latticePages displaying...

SVP, a basis of a vector space V and a norm N (often L2) are given for a lattice L and one must find the shortest non-zero vector in V, as measured by...

the lattice is 1). Equivalently, Γ8 is self-dual, meaning it is equal to its dual lattice. It is even, meaning that the norm of any lattice vector is even...

structure of gradation Normed vector space, a vector space on which a norm is defined Hilbert space Ordered vector space, a vector space equipped with a...

and meet – Concept in order theory Normed lattice Vector lattice – Partially ordered vector space, ordered as a latticePages displaying short descriptions...

normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and...

Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces...

number of lattice vectors of squared norm 2n. In the Leech lattice, there are 196560 vectors of squared norm 4, 16773120 vectors of squared norm 6, 398034000...

primitive vectors for a given Bravais lattice is not unique. A fundamental aspect of any Bravais lattice is that, for any choice of direction, the lattice appears...

framework is more involved than in the normed case. Covariance and contravariance of vectors Dual module Dual norm Duality (mathematics) Duality (projective...

last normed division algebra over the real numbers. The next extension gives the sedenions, which have zero divisors and so cannot be a normed division...

first basis vector is no more than c 1 {\displaystyle c_{1}} times as long as a shortest vector in the lattice, the second basis vector is likewise within...

convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can...

topological vector spaces, which include function spaces, inner product spaces, normed spaces, Hilbert spaces and Banach spaces. In this article, vectors are...

Every normed vector space has a natural topological structure: the norm induces a metric and the metric induces a topology. This is a topological vector space...

definite lattice is the lowest nonzero norm. Lattices are often embedded in a real vector space with a symmetric bilinear form. The lattice is positive...

complete vector lattice under its canonical ordering. The order dual of a vector lattice is an order complete vector lattice. The order dual of a vector lattice...

Topological vector space: a vector space whose M has a compatible topology. Normed vector space: a vector space with a compatible norm. If such a space...

assumption that the shortest vector problem (SVP) is hard in these ideal lattices. In general terms, ideal lattices are lattices corresponding to ideals in...

A distributive lattice is complemented if and only if it is bounded and relatively complemented. The lattice of subspaces of a vector space provide an...

8n dimensional lattice with no norm 1 vectors, where the vertices of each line are the two even lattices associated to the odd lattice. There may be several...

topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that are complete with respect to the metric induced by the norm). All...

norm – Norm on a vector space of matrices Minkowski functional – Function made from a set Norm (mathematics) – Length in a vector space Normed vector...

lattice (the absolute value of the determinant of any of its bases). Suppose that L is a lattice of determinant d(L) in the n-dimensional real vector...

where K is any reciprocal lattice vector (see figure at right). Therefore, wave vectors that differ by a reciprocal lattice vector are equivalent, in the...

of a lattice is a function whose coefficients give the number of vectors of a given norm. One can associate to any (positive-definite) lattice Λ a theta...

such as various restrictions on f-vectors of convex simplicial polytopes, to this more general setting. The face lattice of a convex polytope, consisting...