What does vector field mean?
Definitions for vector field
vec·tor field
This dictionary definitions page includes all the possible meanings, example usage and translations of the word vector field.
Wiktionary
vector fieldnoun
A construction in which each point in a Euclidean space is associated with a vector; a function whose range is a vector space.
vector fieldnoun
A function which associates, to each point on a surface, a vector in the tangent plane of that point.
Wikidata
Vector field
In vector calculus, a vector field is an assignment of a vector to each point in a subset of Euclidean space. A vector field in the plane, for instance, can be visualized as a collection of arrows with a given magnitude and direction each attached to a point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point. The elements of differential and integral calculus extend to vector fields in a natural way. When a vector field represents force, the line integral of a vector field represents the work done by a force moving along a path, and under this interpretation conservation of energy is exhibited as a special case of the fundamental theorem of calculus. Vector fields can usefully be thought of as representing the velocity of a moving flow in space, and this physical intuition leads to notions such as the divergence and curl. In coordinates, a vector field on a domain in n-dimensional Euclidean space can be represented as a vector-valued function that associates an n-tuple of real numbers to each point of the domain. This representation of a vector field depends on the coordinate system, and there is a well-defined transformation law in passing from one coordinate system to the other. Vector fields are often discussed on open subsets of Euclidean space, but also make sense on other subsets such as surfaces, where they associate an arrow tangent to the surface at each point.
Numerology
Chaldean Numerology
The numerical value of vector field in Chaldean Numerology is: 3
Pythagorean Numerology
The numerical value of vector field in Pythagorean Numerology is: 2
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"vector field." Definitions.net. STANDS4 LLC, 2024. Web. 27 Apr. 2024. <https://www.definitions.net/definition/vector+field>.
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