vector field - meaning and definition. What is vector field
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What (who) is vector field - definition


Vector field         
  • Vector fields are commonly used to create patterns in [[computer graphics]]. Here: abstract composition of curves following a vector field generated with [[OpenSimplex noise]].
  • streamline]]s showing a [[wingtip vortex]].
  • A vector field that has circulation about a point cannot be written as the gradient of a function.
  • Magnetic]] field lines of an iron bar ([[magnetic dipole]])
  • A vector field on a [[sphere]]
ASSIGNMENT OF A VECTOR TO EACH POINT IN A SUBSET OF EUCLIDEAN SPACE
Vector fields; Vector field on a manifold; Vector-field; Tangent bundle section; Tangent Bundle Section; Gradient vector field; Gradient flow; Vector plot; Vector Field; Vectorfield; Index of a vector field; F-related; Vector point function; Operations on vector fields; Complete vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For instance, a vector field in the plane can be visualised as a collection of arrows with a given magnitude and direction, each attached to a point in the plane.
https://en.wikipedia.org/wiki/Vector_field
Conservative vector field         
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  • The above vector field <math>\mathbf{v} = \left( - \frac{y}{x^2 + y^2},\frac{x}{x^2 + y^2},0 \right)</math> defined on <math>U = \R^3 \setminus \{ (0,0,z) \mid z \in \R \}</math>, i.e., <math>\R^3</math> with removing all coordinates on the <math>z</math>-axis (so not a simply connected space), has zero curl in <math>U</math> and is thus irrotational. However, it is not conservative and does not have path independence.
  • Line integral paths used to prove the following statement: if the line integral of a vector field is path-independent, then the vector field is a conservative vector field.
  • Depiction of two possible paths to integrate. In green is the simplest possible path; blue shows a more convoluted curve
CONCEPT IN VECTOR CALCULUS
Irrotational; Irrotational field; Gradient field; Potential vector field; Conservative field; Curl free field; Curl-free vector field; Irrotational vector field; Irrotational flow; Irrotational Flow
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 that its line integral is path independent; the choice of any path between two points does not change the value of the line integral.
https://en.wikipedia.org/wiki/Conservative_vector_field
Killing vector field         
  • The Killing field on the circle and flow along the Killing field (enlarge for animation)
  • Killing field on the upper-half plane model, on a semi-circular selection of points. This Killing vector field generates the special conformal transformation. The colour indicates the magnitude of the vector field at that point.
  • Killing field on the sphere. This Killing vector field generates rotation around the z-axis. The colour indicates the height of the base point of each vector in the field. Enlarge for animation of flow along Killing field.
VECTOR FIELD ON A RIEMANNIAN MANIFOLD THAT PRESERVES THE METRIC
Killing vector; Killing vector fields; Killing vectors; Killing symmetry; Killing Vectors; Killing equation
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 manifold) that preserves the metric. Killing fields are the infinitesimal generators of isometries; that is, flows generated by Killing fields are continuous isometries of the manifold.
https://en.wikipedia.org/wiki/Killing_vector_field
Pronunciation examples for vector field
1. And what this vector field shows you,
Soccermatics _ David Sumpter _ Talks at Google
2. of vector field, this type of flow field approach,
Soccermatics _ David Sumpter _ Talks at Google
3. Technically speaking, what the Hairy Ball theorem says is that a continuous vector field
The Hairy Ball Theorem
4. velocity of wind along the surface of the earth is a vector field, so the Hairy Ball
The Hairy Ball Theorem
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