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Concept in 3-dimensional geometry
geometry and vector calculus, an area vector is a vector combining an area quantity with a direction, thus representing an oriented area in three dimensions
Vector_area
Algebraic structure in linear algebra
operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces
Vector_space
Amount of charge flowing through a unit cross-sectional area per unit time
unit time) that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the current density
Current_density
Mass of a substance which passes per unit of time
pipe, the area is the cross-section of the pipe, at the section considered. The vector area is a combination of the magnitude of the area through which
Mass_flow_rate
Mathematical concept applicable to physics
in applied mathematics and vector calculus which has many applications in physics. For transport phenomena, flux is a vector quantity, describing the magnitude
Flux
Geometric object that has length and direction
physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude
Euclidean_vector
Circulation density in a vector field
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
Curl_(mathematics)
Mathematical operation on vectors in 3D space
product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional
Cross_product
Mathematical algorithm for calculating area of a simple polygon
the vertices are not coplanar this computes the vector area enclosed by the loop, i.e. the projected area or "shadow" in the plane in which it is greatest)
Shoelace_formula
Broad concept generalizing scalars in mathematics and physics
In mathematics and physics, a vector is a generalization of a single number. It may denote a vector quantity, i.e., physical quantity that cannot be expressed
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Set of methods for supervised statistical learning
In machine learning, a support vector machine (SVM) or support vector network is a supervised max-margin model with associated learning algorithms that
Support_vector_machine
Term from classical mechanics
areal speed) is this region's area divided by the time interval Δt in the limit that Δt becomes vanishingly small. The vector direction is postulated to
Areal_velocity
Measure of directional electromagnetic energy flux
physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or power
Poynting_vector
Volume of fluid which passes per unit time
The vector area is a combination of the magnitude of the area through which the volume passes through, A, and a unit vector normal to the area, n ^ {\displaystyle
Volumetric_flow_rate
Measure of electric field through surface
electric field is uniform, the electric flux passing through a surface of vector area A is Φ E = E ⋅ A = E A cos θ , {\displaystyle \Phi _{\text{E}}=\mathbf
Electric_flux
Assignment of a vector to each point in a subset of Euclidean space
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
Vector_field
Concept in classical electromagnetism
the curve C) dS is the vector area of an infinitesimal element of surface S (that is, a vector with magnitude equal to the area of the infinitesimal surface
Ampère's_circuital_law
Area interpreted positively or negatively
1 δ b 1 ) . {\displaystyle =(a_{1},\ {\frac {1}{\delta }}b_{1}).} Vector area Volume form Signed distance Signed measure Signed volume Høyrup, Jens
Signed_area
Measurable property of a material or system
where n is the numerical value and kg is the unit symbol (for kilogram). Vector quantities have, besides numerical value and unit, direction or orientation
Physical_quantity
Use of coordinates for representing vectors
Vector notation In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more
Vector_notation
Surface integral of the magnetic field
magnetic field is constant, the magnetic flux passing through a surface of vector area S is Φ B = B ⋅ S = B S cos θ , {\displaystyle \Phi _{B}=\mathbf {B}
Magnetic_flux
Force distributed over an area
{\displaystyle A} is the area of the surface on contact. Pressure is a scalar quantity. It relates the vector area element (a vector normal to the surface)
Pressure
Facet of ballistics and aeronautics
Thrust vectoring, also known as thrust vector control (TVC), is the ability of an aircraft, rocket or other vehicle to manipulate the direction of the
Thrust_vectoring
Vector operator in vector calculus
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
Divergence
Mathematical operation in linear algebra
represented by capital letters in bold, e.g. A; vectors in lowercase bold, e.g. a; and entries of vectors and matrices are italic (they are numbers from
Matrix_multiplication
Two-dimensional vector image file format
Scalable Vector Graphics (SVG) is an XML-based vector graphics format for defining two-dimensional graphics, having support for interactivity and animation
SVG
Algebra associated to any vector space
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle
Exterior_algebra
Agent that carries and transmits pathogens
In epidemiology, a disease vector is any living agent that carries and transmits an infectious pathogen such as a parasite or microbe, to another living
Disease_vector
Index of articles associated with the same name
In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles:
Vector_multiplication
Class of routing protocols
was implemented more widely in local area networks with the Routing Information Protocol (RIP). Distance-vector routing protocols use the Bellman–Ford
Distance-vector routing protocol
Distance-vector_routing_protocol
Vector space with a notion of nearness
A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar
Topological_vector_space
Sum of directed areas in exterior algebra
degree-zero quantity and a vector as a degree-one quantity, a bivector is of degree two. Bivectors have applications in many areas of mathematics and physics
Bivector
Satellite system
number of turns of the wire, I is the current provided, and A is the vector area of the coil. The dipole interacts with the magnetic field generating
Magnetorquer
Space with topology generated by convex sets
and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS)
Locally convex topological vector space
Locally_convex_topological_vector_space
Topics referred to by the same term
Oriented area may be either of: Vector area Signed area This disambiguation page lists articles associated with the title Oriented area. If an internal
Oriented_area
Concepts from linear algebra
algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by a given linear
Eigenvalues_and_eigenvectors
fluid mechanics. Here t ^ {\displaystyle \mathbf {\hat {t}} \,\!} is a unit vector in the direction of the flow/current/flux. Defining equation (physical chemistry)
List of equations in fluid mechanics
List_of_equations_in_fluid_mechanics
Horizontal angle from north or other reference cardinal direction
is the local area (e.g. a circular area with a 5 km radius at sea level) around an observer on Earth's surface, and the reference vector points to true
Azimuth
Magnetic analogue of the electric dipole
moment is the vector sum of the moments of individual turns. If the solenoid has N identical turns (single-layer winding) and vector area S, m = N I S
Magnetic_dipole
Definite integral of a scalar or vector field along a path
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
Line_integral
Property determining comparison and ordering
all Euclidean vectors have a magnitude (see above). However, a vector in an abstract vector space does not possess a magnitude. A vector space endowed
Magnitude_(mathematics)
Basic law of electromagnetism
bounded by the closed loop ∂Σ and dl is an infinitesimal vector element along that loop. The vector area element dA is perpendicular to the surface and oriented
Faraday's_law_of_induction
Algebraic object with geometric applications
of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There
Tensor
Equations describing classical electromagnetism
{S} ,} where dS denotes the differential vector element of surface area S, normal to surface Σ. (Vector area is sometimes denoted by A rather than S,
Maxwell's_equations
Other frequently used formulas for the area of a triangle use trigonometry, side lengths (Heron's formula), vectors, coordinates, line integrals, Pick's
Area_of_a_triangle
Closed surface in three-dimensional space
a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, electric field, or
Gaussian_surface
Obsolete XML-based vector graphics format
the same time other competing W3C submissions were received in the area of web vector graphics, such as Precision Graphics Markup Language (PGML) from Adobe
Vector_Markup_Language
Operation in calculus
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
Integral
Russian government public health agency
though the nature of any ongoing research in this area is uncertain. As of April 2022 the Vector Institute is the Russian site for the WHO H5 Reference
State Research Center of Virology and Biotechnology VECTOR
State_Research_Center_of_Virology_and_Biotechnology_VECTOR
U.S. Air Force facility in Nevada
Commons has media related to Area 51. Las Vegas sectional aeronautical chart, centered on Groom Lake—Federal Aviation Administration at SkyVector.com
Area_51
Vector quantity describing mass flow rate through a given area
pipe, the area is the cross-section of the pipe, at the section considered. The vector area is a combination of the magnitude of the area through which
Mass_flux
Vector behavior under coordinate changes
Briefly, a contravariant vector is a list of numbers that transforms oppositely to a change of basis, and a covariant vector is a list of numbers that
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Speed and direction of a motion
physical objects. Velocity is a vector quantity, meaning that both magnitude and direction are needed to define it (velocity vector). The scalar absolute value
Velocity
Dense urban core together with its satellite cities
past, present and future population and job distributions. It is based on vector field calculations obtained by assuming that, in a given space, all inhabitants
Metropolitan_area
4D analogue of electric current density
current density, with the dimension of electric charge per time per area. Also known as vector current, it is used in the context of four-dimensional spacetime
Four-current
Branch of mathematics
+a_{n}x_{n},} and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear
Linear_algebra
New Zealand electricity distribution company
Vector Limited is a New Zealand energy company, which runs a portfolio of businesses delivering energy and communication services across Australasia and
Vector_Limited
countries and 13 dependencies, based on data calculated in 2000 from the World Vector Shoreline, United States Defense Mapping Agency, 1989. It may include territories
List of countries and dependencies by length of coastline
List_of_countries_and_dependencies_by_length_of_coastline
German software company
Vector Informatik develops software tools and components for networking of electronic systems based on the serial bus systems CAN, LIN, FlexRay, MOST,
Vector_Informatik
Three-dimensional analog of the Pythagorean theorem
Johann Faulhaber (1580–1635) and René Descartes (1596–1650). Vector area and projected area Bivector Lévy-Leblond, Jean-Marc (2020). "The Theorem of Cosines
De_Gua's_theorem
Lists UK postcode map Business Lists UK postcode map FREE Vector UK Postcode Maps PostcodeArea - Demographics, maps, crime rates, house prices and local
List of postcode areas in the United Kingdom
List_of_postcode_areas_in_the_United_Kingdom
Generalization of boundedness
related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be
Bounded set (topological vector space)
Bounded_set_(topological_vector_space)
Property of space that quantifies the magnetic influence at a given location
unit area) transmitted this way is called the poynting vector, S, which depends on the magnetic field as the cross product: The Poynting vector (power
Magnetic_field
Normed vector space that is complete
normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is
Banach_space
Element in Riemannian geometry
vanishes. In such a situation, the mean curvature vector is seen as entirely governing how the surface area of a submanifold is modified by a deformation
First variation of area formula
First_variation_of_area_formula
Formulas about vectors in three-dimensional Euclidean space
The following are important identities in vector algebra. Identities that only involve the magnitude of a vector ‖ A ‖ {\displaystyle \|\mathbf {A} \|} and
Vector_algebra_relations
Approximate nearest neighbor search algorithm
searching vector data. In these systems, an item such as a document, image, song, or user profile is represented by a list of numbers called a vector. Items
Hierarchical navigable small world
Hierarchical_navigable_small_world
Integration over a non-flat region in 3D space
formula for the area of a surface described this way. One can recognize the vector in the second-last line above as the normal vector to the surface.
Surface_integral
Property of a mathematical space
dimension of a vector space is the number of vectors in any basis for the space, i.e. the number of coordinates necessary to specify any vector. This notion
Dimension
is an extension of vector algebra, providing additional algebraic structures on vector spaces, with geometric interpretations. Vector algebra uses all dimensions
Comparison of vector algebra and geometric algebra
Comparison_of_vector_algebra_and_geometric_algebra
Visual aid to depiction of a vector field
visual aid for visualizing vector fields. It consists of an imaginary integral curve which is tangent to the field vector at each point along its length
Field_line
Specialized notation for multivariable calculus
respect to a vector as a column vector or a row vector. Both of these conventions are possible even when the common assumption is made that vectors should be
Matrix_calculus
Four-dimensional number system
Quaternions can be used to represent vectors in three-dimensional space, which provides a definition of the quotient of two vectors. Quaternions were first described
Quaternion
American diversified holding company
Vector Group Ltd. was an American diversified holding company with two major businesses: Liggett Group (tobacco) and New Valley (real estate). In August
Vector_Group
American ultralight aircraft
The Aerodyne Systems Vector is a family of American ultralight aircraft that was designed by Berndt Petterson, Mike McCarron and Paul Yarnell and produced
Aerodyne_Systems_Vector
Transport of dissolved species from the highest to the lowest concentration region
derivatives. Flux is a vector J {\displaystyle \mathbf {J} } representing the quantity and direction of transfer. Given a small area Δ S {\displaystyle \Delta
Diffusion
Standard for encoding geographical information
disadvantages to using a raster or vector data model to represent reality: Raster datasets record a value for all points in the area covered which may require
GIS_file_format
A number of vector graphics editors exist for various platforms. Potential users of these editors will make comparisons based on factors such as the availability
Comparison of vector graphics editors
Comparison_of_vector_graphics_editors
Electromagnetic phenomenon
whether electric or magnetic, is characterized by its dipole moment, a vector quantity. Electric dipoles produce an electric field and experience forces
Dipole
Apparent paradox with Faraday's law of induction
velocity v for a short time d t {\displaystyle dt} , it sweeps out a vector area vector d A = v d t × d ℓ {\displaystyle d\mathbf {A} =\mathbf {v} \,dt\times
Faraday_paradox
Standardized means of organizing and storing digital images
lossy compression or lossless compression. For graphic design applications, vector formats are often used. Some image file formats support transparency. Raster
Image_file_format
Four-vector that is analogous to classical acceleration
four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see three-acceleration
Four-acceleration
Geometry problem
line and n {\displaystyle n} the vector ( a , b ) {\displaystyle (a,b)} starting at point Q {\displaystyle Q} . The vector n is perpendicular to the line
Distance from a point to a line
Distance_from_a_point_to_a_line
Mathematical operation on vector spaces
{\displaystyle V\otimes W} of two vector spaces V {\displaystyle V} and W {\displaystyle W} (over the same field) is a vector space to which is associated
Tensor_product
Navigation service provided to aircraft by air traffic control
Aircraft vectoring is a navigation service provided to aircraft by air traffic control. The controller decides on a particular airfield traffic pattern
Aircraft_vectoring
Computer company
microprocessor, the Vector 1, was introduced in 1977. There were several Vector Graphic models produced. The Vector 1+ had a floppy disk drive. The Vector Graphic
Vector_Graphic
Size of a two-dimensional surface
dx\,dy.} An even more general formula for the area of the graph of a parametric surface in the vector form r = r ( u , v ) , {\displaystyle \mathbf {r}
Area
Equation describing the transport of some quantity
energy flux (transfer of energy per unit cross-sectional area per unit time) as a vector, An important practical example is the flow of heat. When heat
Continuity_equation
their transformation properties (i.e. whether the quantity is a scalar, vector, matrix or tensor), and whether the quantity is conserved. List of photometric
List_of_physical_quantities
Type of display device
for all images. The beam skips over dark areas of the image without visiting their points. Some refresh vector displays use a normal phosphor that fades
Vector_monitor
Conversion of raster graphics into vector graphics
graphics, image tracing, raster-to-vector conversion or raster vectorization is the conversion of raster graphics into vector graphics. An image does not have
Image_tracing
mathematical one-to-one property. The vector formulation makes it possible to use standard 3D vector algebra, and thus n-vector is well-suited for mathematical
Horizontal position representation
Horizontal_position_representation
Classical quantization technique from signal processing
Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the
Vector_quantization
Area of mathematics using condensed sets
geometry. In condensed mathematics, liquid vector spaces are alternatives to complete topological vector spaces, the category of which has better abstract
Condensed_mathematics
Element of an exterior algebra
algebra Λ(V) of a vector space V. This algebra is graded, associative and alternating, and consists of linear combinations of simple k-vectors (also known as
Multivector
n-plane segment of unit area in an n-dimensional vector space. A vector manifold is a special set of vectors in the UGA. These vectors generate a set of linear
Universal_geometric_algebra
Mathematical measure of how much a curve or surface deviates from flatness
rate of change of the direction of the tangent line, or the unit tangent vector, of the curve per unit distance along the curve. Curvature is expressed
Curvature
Counts 0s of a vector field on a differentiable manifold using its Euler characteristic
important theorem in differential topology that relates zeros of continuous vector field on compact differential manifold to Euler characteristic of that manifold
Poincaré–Hopf_theorem
Vector Pipeline L.P. is a 348-mile-long natural gas pipeline which transports approximately 1 billion cubic feet (28,000,000 m3) per day of natural gas
Vector_Pipeline
and their notations. Note that bold text indicates that the quantity is a vector. List of letters used in mathematics and science Glossary of mathematical
List of common physics notations
List_of_common_physics_notations
travel, tourism, insurance
VECTOR AREA
VECTOR AREA
Boy/Male
American, British, Christian, Danish, Dutch, English, Finnish, French, German, Greek, Hindu, Indian, Irish, Jamaican, Latin, Romanian, Slovenia, Spanish, Swedish, Swiss, Tamil, Ukrainian
Victorious; Conqueror; Winner; Champion; One who Conquers; Victory
Boy/Male
Christian & English(British/American/Australian)
Steadfast
Male
Greek
(á¼ÎºÏ„ωÏ) Variant spelling of Greek Hektor, EKTOR means "defend; hold fast."
Boy/Male
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Greek, Italian, Latin, Portuguese, Shakespearean, Spanish
Steadfast; Anchor; Holds Fast; Star; Coined from Esther Vanhomrigh; Tenacious; Defend; Hold Fast; Coined from Esther Vanho
Male
Scandinavian
 Scandinavian form of Roman Latin Victor, VIKTOR means "conqueror." Compare with another form of Viktor.
Boy/Male
Spanish
Victor.
Boy/Male
Latin American Spanish
Conqueror.
Boy/Male
English American
Doctor; teacher.
Surname or Lastname
Scottish
Scottish : Anglicized form of the Gaelic personal name Eachann (earlier Eachdonn, already confused with Norse Haakon), composed of the elements each ‘horse’ + donn ‘brown’.English : found in Yorkshire and Scotland, where it may derive directly from the medieval personal name. According to medieval legend, Britain derived its name from being founded by Brutus, a Trojan exile, and Hector was occasionally chosen as a personal name, as it was the name of the Trojan king’s eldest son. The classical Greek name, HektÅr, is probably an agent derivative of Greek ekhein ‘to hold back’, ‘hold in check’, hence ‘protector of the city’.German, French, and Dutch : from the personal name (see 2 above). In medieval Germany, this was a fairly popular personal name among the nobility, derived from classical literature. It is a comparatively rare surname in France.
Boy/Male
Christian & English(British/American/Australian)
Conqueror
Male
Arthurian
, sir Hector de Maris; (defender).
Male
Portuguese
Galician-Portuguese form of Roman Latin Victor, VITOR means "conqueror."
Male
English
Short form of English Sylvester, VESTER means "from the forest."
Male
English
 Anglicized form of Scottish Gaelic Eachann, HECTOR means "brown horse." Compare with another form of Hector.
Male
English
Roman Latin name VICTOR means "conqueror."Â
Male
Portuguese
Portuguese form of Latin Hector, HEITOR means "defend; hold fast."
Boy/Male
Australian, Basque, Czech, Czechoslovakian, Danish, Finnish, French, German, Hungarian, Latin, Polish, Slovenia, Swedish, Swiss, Ukrainian
The Conqueror; Victory; Victorious; Conquer
Boy/Male
Arthurian Legend
Father of Arthur.
Male
Russian
(Cyrillic Виктор): Slavic form of Roman Latin Victor, VIKTOR means "conqueror." In use by the Bulgarians, Russians and Serbians. Compare with another form of Viktor.
Boy/Male
Spanish American Shakespearean Greek Latin
Tenacious.
VECTOR AREA
VECTOR AREA
VECTOR AREA
VECTOR AREA
VECTOR AREA
VECTOR AREA
VECTOR AREA
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