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)...

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...

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...

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...

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...

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...

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...

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...

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...

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 + ∂...

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

field (or sometimes of a vector field, as in the Navier–Stokes equations); the divergence of a vector field; or the curl (rotation) of a vector field...