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 pseudo-Riemannian manifold...

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

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...

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...

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

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

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)...

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

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...

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...

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

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...

example of a vector bundle (which is a fiber bundle whose fibers are vector spaces). A section of T M {\displaystyle TM} is a vector field on M {\displaystyle...

∇ {\displaystyle \nabla } . Then a vector field X {\displaystyle X} is said to be parallel if for any vector field Y {\displaystyle Y} , ∇ Y X = 0 {\displaystyle...

curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes...

In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters...

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...

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...

presents an introduction to the covariant derivative of a vector field with respect to a vector field, both in a coordinate-free language and using a local...

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...

vector field is a concept that refers to a vector field that maintains the same properties in all directions at each point in space. A vector field V...

returned vector field is equal to the vector field of the scalar Laplacian applied to each vector component. The vector Laplacian of a vector field A {\displaystyle...

property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface...

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