In mathematics, convenient vector spaces are locally convex vector spaces satisfying a very mild completeness condition. Traditional differential calculus...

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...

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...

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

tangent space at x {\displaystyle x} are called the tangent vectors at x {\displaystyle x} . This is a generalization of the notion of a vector, based...

column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The column space of...

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase...

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...

classical Euclidean vector spaces, examples of Hilbert spaces include spaces of square-integrable functions, spaces of sequences, Sobolev spaces consisting of...

constructs a quotient space of the original seminormed vector space, and this quotient is a normed vector space. It inherits several convenient properties from...

transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation...

only handle numerical features. A numeric feature can be conveniently described by a feature vector. One way to achieve binary classification is using a linear...

Bounded set (topological vector space) – Generalization of boundedness Locally convex topological vector space – Vector space with a topology defined by...

space Symplectic space (disambiguation) T2 space Teichmüller space Tensor space Topological space Topological vector space Total space Uniform space Vector...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

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...

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

or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol...

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

orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows...

Quaternions provide a definition of the quotient of two vectors in a three-dimensional space. Quaternions are generally represented in the form a + b...

In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's...

analysis, a differentiable vector-valued function from Euclidean space is a differentiable function valued in a topological vector space (TVS) whose domains...

Every first-countable space (and thus every metrizable space) is N {\displaystyle N} -sequential. There exist topological vector spaces that are sequential...

meaning in the group theory. Rotations of (affine) spaces of points and of respective vector spaces are not always clearly distinguished. The former are...

photons, the space and time components are equal, E/c must therefore be equated with the time component of the spacetime momentum vector. Photons travel...

to variational problems Stampacchia Medal Fermat Prize Convenient vector space Variational vector field Whereas elementary calculus is about infinitesimally...

In classical electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field...

versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically...

experiences of everyday life. Single locations in Euclidean 4D space can be given as vectors or 4-tuples, i.e., as ordered lists of numbers such as (x, y...