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...
2 KB (210 words) - 20:36, 15 December 2022
convex vector lattice Normed lattice Ordered vector space – Vector space with a partial order Pseudocomplement Riesz space – Partially ordered vector space...
4 KB (612 words) - 02:47, 18 September 2024
functional analysis and order theory, a Banach lattice (X,‖·‖) is a complete normed vector space with a lattice order, ≤ {\displaystyle \leq } , such that...
4 KB (466 words) - 02:33, 27 February 2024
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...
28 KB (3,660 words) - 18:18, 23 June 2025
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...
22 KB (3,576 words) - 20:57, 19 June 2025
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...
10 KB (2,684 words) - 04:26, 1 June 2025
Banach space (redirect from Complete normed vector space)
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...
102 KB (17,049 words) - 16:58, 14 April 2025
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...
28 KB (4,307 words) - 20:10, 30 June 2025
and meet – Concept in order theory Normed lattice Vector lattice – Partially ordered vector space, ordered as a latticePages displaying short descriptions...
1 KB (171 words) - 16:31, 30 April 2024
of a lattice Fréchet lattice – Topological vector lattice Normed lattice Vector lattice – Partially ordered vector space, ordered as a latticePages displaying...
7 KB (974 words) - 22:37, 21 January 2023
Riesz space (redirect from Lattice-ordered vector space)
Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces...
31 KB (5,296 words) - 11:25, 31 October 2024
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...
22 KB (2,438 words) - 14:16, 31 May 2025
topological vector spaces, which include function spaces, inner product spaces, normed spaces, Hilbert spaces and Banach spaces. In this article, vectors are...
88 KB (11,598 words) - 03:57, 7 July 2025
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...
14 KB (1,566 words) - 03:26, 17 March 2025
Dual space (redirect from Dual vector space)
framework is more involved than in the normed case. Covariance and contravariance of vectors Dual module Dual norm Duality (mathematics) Duality (projective...
45 KB (6,865 words) - 10:32, 17 March 2025
Quaternion (redirect from Vector quaternion)
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...
97 KB (12,730 words) - 06:25, 7 July 2025
assumption that the shortest vector problem (SVP) is hard in these ideal lattices. In general terms, ideal lattices are lattices corresponding to ideals in...
39 KB (6,061 words) - 05:23, 17 June 2024
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...
15 KB (2,154 words) - 23:50, 19 June 2025
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...
103 KB (13,546 words) - 12:16, 1 May 2025
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...
15 KB (903 words) - 08:06, 14 January 2025
convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can...
58 KB (10,568 words) - 04:52, 2 July 2025
Order dual (functional analysis) (redirect from Minimal vector lattice)
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...
6 KB (946 words) - 23:07, 2 November 2022
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...
21 KB (2,707 words) - 02:10, 7 June 2025
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...
9 KB (876 words) - 15:48, 30 May 2025
Seminorm (redirect from Locally bounded topological vector space)
norm – Norm on a vector space of matrices Minkowski functional – Function made from a set Norm (mathematics) – Length in a vector space Normed vector...
32 KB (6,145 words) - 15:28, 13 May 2025
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...
19 KB (2,350 words) - 11:23, 30 June 2025
some fundamental results in the theory of normed vector lattices, especially in Dedekind complete vector lattices called "K-spaces" which are now referred...
16 KB (1,258 words) - 22:27, 4 May 2025
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...
1 KB (194 words) - 06:36, 27 June 2024
Fréchet space (redirect from Countably-normed space)
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...
29 KB (5,027 words) - 23:19, 9 May 2025
Eulerian poset (redirect from Eulerian lattice)
such as various restrictions on f-vectors of convex simplicial polytopes, to this more general setting. The face lattice of a convex polytope, consisting...
3 KB (407 words) - 23:45, 5 December 2024