This page lists some examples of vector spaces. See vector space for the definitions of terms used on this page. See also: dimension, basis. Notation....

operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces are...

of normed spaces and Banach spaces is a fundamental part of functional analysis, a major subfield of mathematics. A normed vector space is a vector space...

mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X {\displaystyle...

one-dimensional vector spaces are the simple ones. So it is a basic result of linear algebra that any finite-dimensional vector space is the direct sum of simple...

related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that...

spaces and Sobolev spaces. Many topological vector spaces are spaces of functions, or linear operators acting on topological vector spaces, and the topology...

vector, a vector where all components are zero 0 vector space; see Examples of vector spaces 0-velocity surface, or Zero-velocity surface V0 (disambiguation)...

coordinate vector space. Many vector spaces are considered in mathematics, such as extension fields, polynomial rings, algebras and function spaces. The term...

the vector spaces in the above, and many of the major examples are function spaces carrying a topology; the best known examples include Hilbert spaces and...

Euclidean vector spaces, in which the inner product is the dot product or scalar product of Cartesian coordinates. Inner product spaces of infinite dimension...

In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes...

of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces...

Nildimensional space Triviality (mathematics) Examples of vector spaces Field with one element Empty semigroup Zero element List of zero terms David...

sources define affine spaces in terms of the well developed vector space theory. An affine space is a set A together with a vector space A → {\displaystyle...

Examples of generating functions List of space groups Examples of Markov chains Examples of vector spaces Fano plane Frieze group Gray graph Hall–Janko graph...

Vector space model or term vector model is an algebraic model for representing text documents (or more generally, items) as vectors such that the distance...

success of Hilbert space methods ushered in a very fruitful era for functional analysis. Apart from the classical Euclidean vector spaces, examples of Hilbert...

In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space R n {\displaystyle...

spaces through axiomatic theory. Another definition of Euclidean spaces by means of vector spaces and linear algebra has been shown to be equivalent to...

the vector space into a direct sum of vector subspaces, generally indexed by the integers. For "pure" vector spaces, the concept has been introduced in...

idea of a coordinate vector can also be used for infinite-dimensional vector spaces, as addressed below. Let V be a vector space of dimension n over a field...

vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces. Basis vectors find applications in the study of...

theory of vector spaces, a set of vectors is said to be linearly independent if there exists no nontrivial linear combination of the vectors that equals...

finite-dimensional vector spaces. When applied to vector spaces of functions (which are typically infinite-dimensional), dual spaces are used to describe...

transformation, vector space homomorphism, or in some contexts linear function) is a mapping V → W {\displaystyle V\to W} between two vector spaces that preserves...

corresponding Cartesian coordinate system. Canonical units Examples of vector spaces § Generalized coordinate space Roman 2008, p. 47, ch. 1. Axler (2015) p. 39-40...

Fréchet spaces one still has a complete metric, while LF-spaces are complete uniform vector spaces arising as limits of Fréchet spaces. Space (mathematics) –...

(normed vector spaces that are complete with respect to the metric induced by the norm). All Banach and Hilbert spaces are Fréchet spaces. Spaces of infinitely...

mathematics, a symplectic vector space is a vector space V {\displaystyle V} over a field F {\displaystyle F} (for example the real numbers R {\displaystyle...