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...

In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property...

In mathematics, a Killing vector field (often called a Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian...

vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field)...

In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named...

means that, for two vector spaces over a given field and with the same dimension, the properties that depend only on the vector-space structure are exactly...

electric field between atoms is the force responsible for chemical bonding that result in molecules. The electric field is defined as a vector field that...

tuples is called a coordinate vector space. Many vector spaces are considered in mathematics, such as extension fields, polynomial rings, algebras and...

assigning a vector to each point of space, called a vector field (more precisely, a pseudovector field). In electromagnetics, the term magnetic field is used...

In vector calculus, a Laplacian vector field is a vector field which is both irrotational and incompressible. If the field is denoted as v, then it is...

In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional...

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

mathematical field of differential topology, the Lie bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector fields, is an...

scalar field (that is, a function of position which returns a scalar as a value), or a vector field (that is, a function which returns a vector as value)...

radius vector connecting the origin to the point in question, while ϕ {\displaystyle \phi } is the angle between the projection of the radius vector onto...

In physics and mathematics, a symplectic vector field is one whose flow preserves a symplectic form. That is, if ( M , ω ) {\displaystyle (M,\omega )}...

letters represent vectors and E is the electric field vector; H is the magnetic field's auxiliary field vector or magnetizing field. This expression is...

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 source...

In science, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. An example...

theorem of vector calculus states that certain differentiable vector fields can be resolved into the sum of an irrotational (curl-free) vector field and a...

In vector calculus, a complex lamellar vector field is a vector field which is orthogonal to a family of surfaces. In the broader context of differential...

In physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space...

electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: ∇ × A = B {\textstyle...

fundamental vector fields are an instrument that describes the infinitesimal behaviour of a smooth Lie group action on a smooth manifold. Such vector fields find...

In vector calculus, a Beltrami vector field, named after Eugenio Beltrami, is a vector field in three dimensions that is parallel to its own curl. That...

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

of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension...

three-dimensional Cartesian coordinate variables, the gradient is the vector field: grad ⁡ ( f ) = ∇ f = ( ∂ ∂ x ,   ∂ ∂ y ,   ∂ ∂ z ) f = ∂ f ∂ x i + ∂...

speed) and a vector (a magnitude and a direction, like velocity), a tensor field is a generalization of a scalar field and a vector field that assigns...

physics) Row and column vectors, single row or column matrices Vector quantity Vector space Vector field, a vector for each point Vector (molecular biology)...