Examples of vector spaces information

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....

complex vector space are kinds of vector spaces based on different kinds of scalars: real coordinate space or complex coordinate space. Vector spaces generalize...

well-known examples of TVSs. Many topological vector spaces are spaces of functions, or linear operators acting on topological vector spaces, and the topology...

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...

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...

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)...

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

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

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

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...

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...

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...

qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space. Vectors play an important...

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...

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...

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...

all Banach spaces) can be considered as being generalizations of (pre-)Hilbert spaces. Characterization in terms of series The vector space structure allows...

affine space with a distinguished point O may be identified with its associated vector space (see Affine space § Vector spaces as affine spaces), the preceding...

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

familiar examples of this construction occur when considering vector spaces (modules over a field) and abelian groups (modules over the ring Z of integers)...

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

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

span) of a set S of vectors (from a vector space), denoted span(S), is defined as the set of all linear combinations of the vectors in S. For example, two...

topological vector space to possess. The notions of completeness for normed spaces and metrizable TVSs, which are commonly defined in terms of completeness of a...

Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional...