Linked from

The 47 pages that link to Vector field, each with the reason it gives.

• Electric fieldNarrower topic: Electric fields are spatially varying vectors, not merely scalar values.

• Magnetic fieldNarrower topic: A magnetic field assigns both magnitude and direction throughout space.

• GradientNarrower topic: The gradient’s output is a vector field over the scalar field’s domain.

• Tangent spaceRelated: Vector fields are sections that assign elements of each tangent space.

• Scalar fieldCompared with: A vector field assigns direction-bearing quantities where a scalar field assigns single values.

• DivergenceNarrower topic: Divergence is defined by how a vector field varies around each point.

• VectorNarrower topic: A vector is one value; a vector field distributes such values across space.

• Gravitational fieldNarrower topic: A gravitational field is one physical example of this broader mathematical structure.

• Line integralNarrower topic: Vector line integrals sample these assigned vectors along a curve.

• Smooth manifoldRelated: Vector fields describe smooth directions of motion over the space.

• Velocity fieldNarrower topic: A velocity field is a vector field whose values represent motion.

• Divergence theoremNarrower topic: The theorem applies to a field whose values define flux and divergence.

• Material derivativeRelated: The same derivative applies componentwise to vector quantities such as velocity.

• ManifoldRelated: Vector fields describe directions of flow across a manifold.

• Current densityNarrower topic: Current density is commonly modeled as a vector field varying through space.

• CurlNarrower topic: Curl acts on vector fields and describes their local variation.

• Stokes' theoremNarrower topic: The theorem applies to vector fields whose curl is integrated over a surface.

• Surface integralRelated: A vector surface integral measures how the field crosses the surface.

• Scientific visualizationRelated: Direction and magnitude fields require visual encodings such as arrows, streamlines, or glyphs.

• Affine connectionRelated: Vector fields are both the inputs to and outputs of the connection's derivative.

• Eulerian descriptionRelated: Velocity and other directional quantities are commonly represented at spatial positions.

• Vector calculusRelated: Divergence, curl, and field integrals operate on vector fields.

• Lie bracketRelated: Vector fields acquire a Lie bracket through the commutator of their actions on functions.

• Tensor fieldBroader topic: It is the simplest non-scalar tensor field and describes directions varying over space.

• Electric fluxNarrower topic: Electric flux is one example of measuring a vector field through a surface.

• Classical field theoryBroader topic: Electric and magnetic fields are familiar examples of vector-valued fields.

• Polarization densityNarrower topic: Polarization density assigns a direction and magnitude throughout a material.

• Vector (physics)Narrower topic: A single vector describes one quantity; a vector field describes its spatial distribution.

• Vector bundleRelated: A vector field is a section of the tangent bundle.

• Gauss's law for magnetismNarrower topic: The magnetic field is a vector field whose divergence the law constrains.

• Magnetic vector potentialNarrower topic: The magnetic vector potential assigns a vector throughout space.

• Poincaré–Hopf theoremNarrower topic: The theorem begins with a smooth field whose isolated zeros contribute the indices.

• Conservative vector fieldNarrower topic: Conservativeness is a special property of vector fields.

• Nonconservative forceNarrower topic: A force is modeled as a vector field whose work can be tested along paths.

• Phase portraitRelated: For continuous systems, its vectors indicate the local direction of trajectories.

• SourceNarrower topic: Sources describe outward emergence within vector fields.

• Flow (mathematics)Narrower topic: The vector field supplies the instantaneous velocity that generates the flow.

• Solenoidal vector fieldNarrower topic: Solenoidality is a constraint on a vector field, not a separate kind of quantity.

• Hairy ball theoremNarrower topic: The theorem rules out a nowhere-zero tangent vector field on even-dimensional spheres.

• Volume integralRelated: Vector-valued volume integrals accumulate vector quantities across a region.

• Bendixson–Dulac theoremRelated: A planar autonomous system defines the flow whose closed trajectories are excluded.

• Vector-valued functionRelated: It extends vector-valued outputs across a spatial domain.

• Eulerian flow fieldNarrower topic: The flow field is a time-dependent vector field with velocity vectors as values.

• Gradient theoremNarrower topic: The gradient of the scalar field is the vector field integrated along the path.

• Displacement current densityNarrower topic: Displacement current density has both magnitude and direction at every point.

• Field lineNarrower topic: Field lines are curves defined by the directions of vectors at each point.

• Three-dimensional system (spatial)Related: It represents spatially distributed quantities such as velocity or force.