• Thumbnail for Vector field
    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...
    28 KB (4,076 words) - 01:44, 23 February 2025
  • 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...
    23 KB (3,529 words) - 10:53, 16 March 2025
  • In mathematics, a Killing vector field (often called a Killing field), named after Wilhelm Killing, is a vector field on a pseudo-Riemannian manifold...
    27 KB (4,724 words) - 05:17, 14 June 2025
  • Thumbnail for Solenoidal vector field
    vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field)...
    4 KB (430 words) - 08:36, 28 November 2024
  • Thumbnail for Vector space
    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...
    88 KB (11,598 words) - 03:57, 7 July 2025
  • Thumbnail for Electric field
    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...
    43 KB (5,520 words) - 08:28, 3 July 2025
  • Thumbnail for Curl (mathematics)
    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...
    34 KB (5,050 words) - 04:31, 3 May 2025
  • In physics and mathematics, a symplectic vector field is one whose flow preserves a symplectic form. That is, if ( M , ω ) {\displaystyle (M,\omega )}...
    2 KB (338 words) - 05:52, 4 March 2024
  • 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...
    44 KB (7,266 words) - 03:08, 20 April 2025
  • In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named...
    8 KB (1,321 words) - 19:22, 3 April 2025
  • Thumbnail for Surface integral
    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)...
    15 KB (2,248 words) - 21:06, 10 April 2025
  • tuples is called a coordinate vector space. Many vector spaces are considered in mathematics, such as extension fields, polynomial rings, algebras and...
    10 KB (2,684 words) - 04:26, 1 June 2025
  • 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...
    7 KB (960 words) - 05:41, 24 June 2025
  • Thumbnail for Magnetic field
    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...
    105 KB (12,969 words) - 07:57, 9 June 2025
  • Thumbnail for Poynting vector
    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...
    33 KB (4,629 words) - 13:32, 2 July 2025
  • Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional...
    22 KB (2,135 words) - 04:00, 8 April 2025
  • Thumbnail for Field (physics)
    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...
    36 KB (4,401 words) - 14:11, 28 June 2025
  • Thumbnail for Vector fields in cylindrical and spherical coordinates
    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...
    10 KB (1,738 words) - 20:51, 11 February 2025
  • Thumbnail for Tangent bundle
    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...
    17 KB (2,949 words) - 23:44, 2 May 2025
  • Thumbnail for Parallel transport
    ∇ {\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...
    20 KB (3,104 words) - 15:23, 13 June 2025
  • 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...
    21 KB (3,183 words) - 03:16, 18 March 2025
  • Thumbnail for Divergence
    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...
    32 KB (4,666 words) - 21:59, 25 June 2025
  • Thumbnail for Tensor field
    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...
    26 KB (4,401 words) - 20:56, 18 June 2025
  • 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...
    9 KB (1,108 words) - 21:08, 13 February 2024
  • 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...
    37 KB (6,455 words) - 10:20, 22 June 2025
  • Del (redirect from Vector differential)
    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...
    22 KB (3,921 words) - 04:13, 10 June 2025
  • Thumbnail for Isotropic 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...
    4 KB (448 words) - 03:41, 28 May 2025
  • 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...
    30 KB (4,682 words) - 23:08, 23 June 2025
  • Flux (redirect from Flux of a vector field)
    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...
    28 KB (3,869 words) - 23:13, 15 May 2025
  • Thumbnail for Magnetic vector potential
    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...
    28 KB (4,378 words) - 22:37, 31 May 2025