In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied...

In mathematics, a set B of elements of a vector space V is called a basis (pl.: bases) if every element of V can be written in a unique way as a finite...

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...

In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization...

mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an...

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...

A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar...

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...

re-formalized to define Euclidean spaces through axiomatic theory. Another definition of Euclidean spaces by means of vector spaces and linear algebra has been...

In mathematics, any vector space V {\displaystyle V} has a corresponding dual vector space (or just dual space for short) consisting of all linear forms...

analysis, a Banach space (/ˈbɑː.nʌx/, Polish pronunciation: [ˈba.nax]) is a complete normed vector space. Thus, a Banach space is a vector space with a metric...

In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance...

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

representation is a real-valued vector that encodes the meaning of the word in such a way that the words that are closer in the vector space are expected to be similar...

on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is called...

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...

notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional...

product V ⊗ W {\displaystyle V\otimes W} of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map V × W...

point, the zero vector is called the origin. Adding a fixed vector to the elements of a linear subspace (vector subspace) of a vector space produces an affine...

space and time in the coordinate form in a four-dimensional real vector space. Points in this space correspond to events in spacetime. In this space,...

Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that...

a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a direct...

length) and direction. Euclidean vectors can be added and scaled to form a vector space. A vector quantity is a vector-valued physical quantity, including...

formalism of vector spaces, with the work of Hermann Grassmann and Giuseppe Peano, the latter of whom first gave the modern definition of vector spaces as an...

In 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...

Euclidean vector space (named here E {\displaystyle E} ), and is denoted by the symbol × {\displaystyle \times } . Given two linearly independent vectors a and...

vector space V {\displaystyle V} by a subspace N {\displaystyle N} is a vector space obtained by "collapsing" N {\displaystyle N} to zero. The space obtained...

mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes...

inherited by the function space. For example, the set of functions from any set X into a vector space has a natural vector space structure given by pointwise...

sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There...