# Vector fields on any smooth manifold M can be thought of as derivations X of the ring of smooth functions on the manifold, and therefore form a Lie algebra under the Lie bracket = XY − YX, because the Lie bracket of any two derivations is a derivation.

Vector calculus ( or vector analysis ) is a branch of mathematics concerned with differentiation and integration of vector fields, primarily in 3 dimensional Euclidean space The term " vector calculus " is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration.

Vector calculus studies various differential operators defined on scalar or vector fields, which are typically expressed in terms of the del operator ().

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.

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 ( a tangent vector ).

Vector fields are one kind of tensor field.

Vector fields are thus contrasted with scalar fields, which associate a number or scalar to every point in space, and are also contrasted with simple lists of scalar fields, which do not transform under coordinate changes.

Vector fields can be constructed out of scalar fields using the gradient operator ( denoted by the del: ∇).

* Vector fields, which associate a vector to every point in space.

Magnetic fields add as vectors. Vector sum of the magnetic field vectors of the stator coils produces a single rotating vector of resulting rotating magnetic field.

Examples of potential and gradient fields in physicsScalar fields ( scalar potentials ) (< span style =" color: yellow "> yellow </ span >): V < sub > G </ sub >-gravitational potential ; W < sub > pot </ sub >-potential energy ; V < sub > C </ sub >-Coulomb potential ; Vector fields ( gradient fields ) (< span style =" color: cyan "> cyan </ span >): a < sub > G </ sub >-gravitational acceleration ; F-force ; E-electric field strength

* Vector fields on spheres

It is known as TeVeS for Tensor / Vector / Scalar and it introduces three different fields in space time to replace the one gravitational field.

Vector fields can have several special points: a stable point, called a sink, that attracts in all directions ( forcing the concentrations to be at a certain value ), an unstable point, either a source or a saddle point which repels ( forcing the concentrations to change away from a certain value ), and a limit cycle, a closed trajectory towards which several trajectories spiral towards ( making the concentrations oscillate ).

Vector gauge theories with massless Dirac fermion fields exhibit chiral symmetry, i. e., rotating the left-handed and the right-handed components independently makes no difference to the theory.

Vector fields that satisfy the conformal Killing equation are exactly those vector fields whose flow preserves the conformal structure of the manifold.

Vector fields can be specified as first order linear partial differential operators, such as

Vector illustrations can have their own color, allowing artists to achieve desired results.

Vector graphics can be created in hardcopy form using a pen plotter, a special type of printer that uses a series of ballpoint and / or felt-tip pens on a servo-driven mount that moves horizontally across the paper, with the plotter moving the paper back and forth through its paper path for vertical movement.

gnuplot can produce output directly on screen, or in many formats of graphics files, including Portable Network Graphics ( PNG ), Encapsulated PostScript ( EPS ), Scalable Vector Graphics ( SVG ), JPEG and many others.

By default, only total delay and minimum bandwidth are considered when EIGRP is started on a router, but an administrator can enable or disable all the K values as needed to consider the other Vector metrics.

Vector processor ( SIMD ) cores can be combined with VLIW architecture as the Fujitsu FR-V, further increasing throughput and speed.

Vector processors can greatly improve performance on certain workloads, notably numerical simulation and similar tasks.

Using the Virtual Vector Architecture, several POWER5 processors can act together as one vector processor.

Vector shapes are supported using a separate vector layer, and can be used to

If we ignore the velocity field, the radial component of Poynting's Vector resulted from the Liénard – Wiechert field can be calculated to be

* Vector signal analyzer ( VSA ) ( Like the SA but it can also perform many more useful digital demodulation functions )

Vector drawings can be imported or directly opened for editing.

Vector features can be made to respect spatial integrity through the application of topology rules such as ' polygons must not overlap '.

Vector data can also be used to represent continuously varying phenomena.

* Vector data can be displayed as vector graphics used on traditional maps, whereas raster data will appear as an image that may have a blocky appearance for object boundaries.

* Vector data can be easier to register, scale, and re-project, which can simplify combining vector layers from different sources.

* Vector data is more compatible with relational database environments, where they can be part of a relational table as a normal column and processed using a multitude of operators.

* Vector file sizes are usually smaller than raster data, which can be tens, hundreds or more times larger than vector data ( depending on resolution ).

* specific file extension, can stand for Aepryus Graph Image or Screen Saver File supported by Aepryus Software, or APM Graph Vector Graphic supported by APM company, or Grace Project File used by 2D plotting software Grace.

It has not been explained why he or the other Dinobots were able to be fitted with personalities which can only be found on Cybertron from Vector Sigma.

Hypertext links in Scalable Vector Graphics can currently be defined as simple XLinks.

Many algorithms, including Support Vector Machines, linear regression, logistic regression, neural networks, and nearest neighbor methods, require that the input features be numerical and scaled to similar ranges ( e. g., to the interval ).

Vector graphics are ideal for simple or composite drawings that need to be device-independent, or do not need to achieve photo-realism.

Vector editors tend to be better suited for graphic design, page layout, typography, logos, sharp-edged artistic illustrations ( e. g. cartoons, clip art, complex geometric patterns ), technical illustrations, diagramming and flowcharting.

Vector data encoding requires less memory and less data storage, in situations where the shapes may need to be resized, as with font typefaces.

In November 2009, it was announced that Vector Capital would be purchasing the remaining shares of common stock in Corel Corporation.

* For the first time since Rodimus Prime in Generation One, Cybertron featured a Prime other than Optimus — Vector Prime, said to be one of the first 13 Transformers ever created.

Vector bundles are almost always required to be locally trivial, however, which means they are examples of fiber bundles.

Hypermedia applications may be developed on embedded devices for the mobile and the Digital signage industries using the Scalable Vector Graphics ( SVG ) specification from W3C ( World Wide Web Consortium ).

In the final steps, two equalities will be used: ( 1 ) A Vector Analysis Equality, ( 2 ) One of Maxwell's Equations.

At the time of its first publication, Vector Prime was extremely controversial among Star Wars fans in that its plot called for the death of Chewbacca, making the Wookiee the first major character from the original trilogy to be permanently killed off in the Expanded Universe novels.