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Vector-based collection of geographic information system (GIS) data about Earth
The Vector Map (VMAP), also called Vector Smart Map, is a vector-based collection of geographic information system (GIS) data about Earth at various levels
Vector_Map
Mathematical parametrization of vector spaces by another space
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space
Vector_bundle
Topics referred to by the same term
Look up vector or vectorial in Wiktionary, the free dictionary. Vector most often refers to: Disease vector, an agent that carries and transmits an infectious
Vector
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
Mathematical operation on vector spaces
product V⊗W of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map V×W→V⊗W that maps a pair (v,w), where
Tensor_product
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 ℝn. A vector field
Vector_field
Mathematical function, in linear algebra
linear map, linear mapping, or linear operator is a particular kind of function between vector spaces, which respects the basic operations of vector addition
Linear_map
Function of two vectors linear in each argument
In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each
Bilinear_map
Map displayed with adjoining small images
Google Maps was one of the first major mapping sites to use this technique. The first tiled web maps used raster tiles, before the emergence of vector tiles
Tiled_web_map
Packets of geographic data in vector format
styled web maps, combining certain benefits of pre-rendered raster map tiles with vector map data. As with the widely used raster tiled web maps, map data is
Vector_tiles
Calculus of vector-valued functions
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional
Vector_calculus
Number of vectors in any basis of the vector space
In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes
Dimension_(vector_space)
Algebraic structure decomposed into a direct sum
mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a
Graded_vector_space
Mathematical operation in linear algebra
A linear map A from a vector space of dimension n into a vector space of dimension m maps a column vector 𝐱=(x1x2⋮xn) onto the column vector
Matrix_multiplication
Mathematics concept
mathematics, the complex conjugate of a complex vector space V {\displaystyle V\,} is a complex vector space V ¯ {\displaystyle {\overline {V}}} that has
Complex conjugate of a vector space
Complex_conjugate_of_a_vector_space
Euclidean space without distance and angles
space is nothing more than a vector space whose origin we try to forget about, by adding translations to the linear maps"). Imagine that Alice knows that
Affine_space
Mathematical representation of absence of a value
be a vector mapped to some null by a function under consideration (such as a quadratic form coming with the vector space, see null vector, a linear mapping
Null_(mathematics)
Standard for encoding geographical information
spatial vector storage Keyhole Markup Language (KML) – XML based open standard (by OpenGIS) for GIS data exchange MapInfo TAB format – MapInfo's vector data
GIS_file_format
Machine learning technique useful for dimensionality reduction
node in the map space is associated with a "weight" vector, which is the position of the node in the input space. While nodes in the map space stay fixed
Self-organizing_map
Linear approximation of smooth maps on tangent spaces
used to push tangent vectors on M {\displaystyle M} forward to tangent vectors on N {\displaystyle N} . The differential of a map φ {\displaystyle \varphi
Pushforward_(differential)
Multivariate derivative (mathematics)
In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) ∇f whose
Gradient
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
Line or vector perpendicular to a curve or a surface
P is a vector perpendicular to the tangent plane of the surface at P. The vector field of normal directions to a surface is known as Gauss map. The word
Normal_(geometry)
Vectors mapped to 0 by a linear map
the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of the co-domain; the
Kernel_(linear_algebra)
Geometric transformation that preserves lines but not angles nor the origin
W the respective associated vector spaces over the field k. A map f : X → Z is an affine map if there exists a linear map mf : V → W such that mf (x −
Affine_transformation
In mathematics, vector space of linear forms
In mathematics, every vector space V {\displaystyle V} has a corresponding dual vector space (or just dual space for short) consisting of all linear forms
Dual_space
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
Branch of mathematics
common to all vector spaces. Linear maps are mappings between vector spaces that preserve the vector-space structure. Given two vector spaces V and W
Linear_algebra
Coordinate change in linear algebra
ordered basis of a vector space of finite dimension n allows representing uniquely any element of the vector space by a coordinate vector, which is a finite
Change_of_basis
Vector space with generalized dot product
space is a real or complex vector space endowed with an operation called an inner product. The inner product of two vectors in the space is a scalar, often
Inner_product_space
Map from a vector space to its underlying field
is a map from a vector space to its underlying field. Elements of this field are called scalars, typically real or complex numbers. If the map is linear
Functional_(mathematics)
Vector space on which a distance is defined
In mathematics, a normed vector space or normed space is a vector space, typically over the real or complex numbers, on which a norm is defined. A norm
Normed_vector_space
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
Induced map between the dual spaces of the two vector spaces
adjoint of a linear map between two vector spaces, defined over the same field, is an induced map between the dual spaces of the two vector spaces. The transpose
Transpose_of_a_linear_map
Collaborative map database
slippy map. Alternatively, a server application converts raw OSM data into vector tiles according to a schema, such as Mapbox Streets, OpenMapTiles, or
OpenStreetMap
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
Vector differential operator
or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by ∇ (the nabla symbol)
Del
Computer graphics images defined by points, lines and curves
Vector graphics are a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as
Vector_graphics
Set of vectors used to define coordinates
In mathematics, a set B of elements of a vector space V is called a basis (pl.: bases) if every element of V can be written in a unique way as a finite
Basis_(linear_algebra)
Mathematical description of spacetime used in relativity
satisfying ΛρμημνΛσν=ηρσ. or Λ, a linear map on the abstract vector space satisfying, for any pair of vectors u, v, η(Λu,Λv)=η(u,v). Then if two different
Minkowski_spacetime
Symbolic depiction of spatial relationships
photos, vector or feature data, existing maps, rectified imagery, digital terrain data, metadata. Anthamatten 2021, pp. 189–197, p. 189 (vector data for
Map
Vector representing the position of a point with respect to a fixed origin
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space.
Position_(geometry)
Tangent spaces of a manifold
tangent vector to each point of a manifold is called a vector field. Specifically, a vector field on a manifold M {\displaystyle M} is a smooth map V : M
Tangent_bundle
realtime routing engine and support for various vector map formats. It features both a 2D and 3D view of map data. Navit supports a variety of operating systems
Navit
Texture mapping technique
property. Normal map reuse is made possible by encoding maps in tangent space. The tangent space is a vector space, which is tangent to the model's surface. The
Normal_mapping
Representation learning technique
representation learning technique that maps complex, high-dimensional data into a lower-dimensional vector space of numerical vectors. It also denotes the resulting
Embedding_(machine_learning)
Submachine gun
The KRISS Vector is a submachine gun developed by the American company KRISS USA, formerly Transformational Defense Industries (TDI). Civilian variants
KRISS_Vector
Method in natural language processing
learning techniques, where words or phrases from the vocabulary are mapped to vectors of real numbers. Methods to generate this mapping include neural networks
Word_embedding
Length in a vector space
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance
Norm_(mathematics)
Matrix consisting of a single row or column
linear map and act on row and column vectors as the linear map's transformation matrix. For a row vector v, the product vM is another row vector p: 𝐯M=𝐩
Row_and_column_vectors
Vector Product Format (VPF) is a military standard for vector-based digital map products produced by the U.S. Department of Defense (DOD). It has been
Vector_Product_Format
Topologically Integrated Geographic Encoding and Referencing (Tiger)/Line 2003 vector map data, and the USGS GeoNames database. Based on the archive of the website
Libre_Map_Project
Differential geometry topic
differential geometry, the Gauss map of a surface is a function that maps each point in the surface to its normal direction, a unit vector that is orthogonal to
Gauss_map
Conjugate homogeneous additive map
Antilinear maps stand in contrast to linear maps, which are additive maps that are homogeneous rather than conjugate homogeneous. If the vector spaces are
Antilinear_map
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
Algebraic operation on coordinate vectors
numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the scalar product of two vectors is the dot product of their
Dot_product
(that is, topological vector spaces), then it makes sense to ask whether all linear maps are continuous. It turns out that for maps defined on infinite-dimensional
Discontinuous_linear_map
Linear map from a vector space to its field of scalars
covector) is a linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers). If V is a vector space over a field
Linear_form
Public domain geographic data collection
Natural Earth's data set contains integrated vector and raster mapping data. The original authors of the map dataset are Tom Patterson and Nathaniel Vaughn
Natural_Earth
Matrix operation which flips a matrix over its diagonal
of infinite dimensional vector spaces). In the finite dimensional case, the matrix representing the transpose of a linear map is the transpose of the
Transpose
Horizontal angle from north or other reference cardinal direction
surface, and the reference vector points to true north. The azimuth is the angle between the north vector and the star's vector on the horizontal plane.
Azimuth
Distance-preserving mathematical transformation
and Y are complex vector spaces then A may fail to be linear as a map over C {\displaystyle \mathbb {C} } . Given two normed vector spaces V {\displaystyle
Isometry
Fundamental space of geometry
vector and has the identity as associated linear map. The inverse isometry is the map v↦O+v. A Euclidean frame (O,e1,…,en) allows defining the map E→ℝnP↦(e1⋅OP→
Euclidean_space
Physical quantities taking values at each point in space and time
by a scalar, vector, spinor, or tensor – that has a value for each point in space and time. An example of a scalar field is a weather map of surface temperatures
Field_(physics)
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)
Counts 0s of a vector field on a differentiable manifold using its Euler characteristic
of the Gauss map from the boundary of Nε to the (n–1)-dimensional sphere. Thus, the sum of the indices is independent of the actual vector field, and depends
Poincaré–Hopf_theorem
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
Open railway mapping software project
started in 2011. The OpenRailwayMap website was launched in mid 2013. The map originally supported both raster tiles and vector tiles, but support for the
OpenRailwayMap
Vector operation
two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector. If the two coordinate
Outer_product
Assignment of vector fields to manifolds
vector-space operations on T x M {\displaystyle T_{x}M} , we use a chart φ : U → R n {\displaystyle \varphi :U\to \mathbb {R} ^{n}} and define a map d
Tangent_space
Mathematical concept
In mathematics, a symplectic vector space is a vector space V over a field F (for example the real numbers ℝ) equipped with a symplectic bilinear form
Symplectic_vector_space
Scalar-valued bilinear function
mathematics, a bilinear form is a bilinear map V × V → K on a vector space V (the elements of which are called vectors) over a field K (the elements of which
Bilinear_form
2007 video game
top of the screen and are represented separately as different icons. A vector map can be displayed on the screen, showing characters' locations and their
Death_to_Spies
Linear map or polynomial function of degree one
affine maps. In linear algebra, a linear function is a map f {\displaystyle f} from a vector space V {\displaystyle \mathbf {V} } to a vector space W
Linear_function
Space with topology generated by convex sets
mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed
Locally convex topological vector space
Locally_convex_topological_vector_space
Map that satisfies a condition similar to that of being an open map
categories of topological vector spaces, all surjective linear operators are necessarily almost open. Given a surjective map f:X→Y, a point x∈X is called
Almost_open_map
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
Vector-valued function of multiple vectors, linear in each argument
Any bilinear map is a multilinear map. For example, any inner product on a R {\displaystyle \mathbb {R} } -vector space is a multilinear map, as is the
Multilinear_map
\mathbb {K} } , is called a vector bornology if B {\displaystyle {\mathcal {B}}} makes the vector space operations into bounded maps. A bornology on a set X
Vector_bornology
Obsolete XML-based vector graphics format
Vector Markup Language (VML) is an obsolete XML-based file format for two-dimensional vector graphics. It was specified in Part 4 of the Office Open XML
Vector_Markup_Language
Design of geospatial data storage
resource data as "faces" (vector polygons), although these were typically derived from raster scans of paper maps. Dual Independent Map Encoding (DIME, US Census
Data_model_(GIS)
Plasmid cloning vector
pUC19 is one of a series of plasmid cloning vectors designed by Joachim Messing and co-workers. The designation "pUC" is derived from the classical "p"
PUC19
Dual pair of vector spaces
𝕂 is a triple (X,Y,b) consisting of two vector spaces, X and Y, over 𝕂 and a non-degenerate bilinear map b:X×Y→𝕂. In mathematics, duality is the study
Dual_system
Dimension of the column space of a matrix
by rg(A), from German Rang. More generally, the rank of a linear map between two vector spaces is the dimension of its image. In this section, we give some
Rank_(linear_algebra)
of topological vector spaces is the category whose objects are topological vector spaces and whose morphisms are continuous linear maps between them. This
Category of topological vector spaces
Category_of_topological_vector_spaces
Exterior algebraic map taking tensors from p forms to n-p forms
star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric
Hodge_star_operator
Similarity measure for number sequences
between two non-zero vectors defined in an inner product space. Cosine similarity is the cosine of the angle between the vectors; that is, it is the dot
Cosine_similarity
Topics referred to by the same term
includes: Kernel (linear algebra) or null space, a set of vectors mapped to the zero vector Kernel (category theory), a generalization of the kernel of
Kernel
Topic in mathematics
mathematics, the complexification of a vector space V over the field of real numbers (a "real vector space") yields a vector space VC over the complex number
Complexification
bilinear maps of topological vector spaces that is weaker than continuity but stronger than separate continuity. Many important bilinear maps that are
Hypocontinuous_bilinear_map
Map from tangent space to the manifold
_{v}(0)=p} with initial tangent vector γ v ′ ( 0 ) = v {\displaystyle \gamma _{v}'(0)=v} . The corresponding exponential map is defined by exp p ( v ) =
Exponential map (Riemannian geometry)
Exponential_map_(Riemannian_geometry)
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
Netherlands-based mapping data company
functionality to include vector maps, turn-by-turn guidance, truck routing, 3D venue maps and augmented reality. Offline Enterprise Maps (for truck attributes
Here_Technologies
Theorem on extension of bounded linear functionals
the extension of bounded linear functionals defined on a vector subspace of some normed vector space to the whole space. In a different guise the theorem
Hahn–Banach_theorem
2D image 2D texture map A texture map with two dimensions, typically indexed by UV coordinates. 2D vector A two-dimensional vector, a common data type
Glossary_of_computer_graphics
Generalization of complex inner products
motivating special case is a sesquilinear form on a complex vector space, V. This is a map V × V → C that is linear in one argument and "twists" the linearity
Sesquilinear_form
Type of display device
A vector monitor, vector display, or calligraphic display is a display device used for computer graphics up through the 1970s. It is a type of CRT, similar
Vector_monitor
Concepts in mathematics
vector field is a map to the tangent space, it represents the tangent vectors to some function at each point. Splitting the tangent vectors into directional
Vector_flow
The MapInfo TAB format is a geospatial vector data format for geographic information systems software. It is developed and regulated by Precisely as a
MapInfo_TAB_format
Vector behavior under coordinate changes
It lives in the dual vector space, and represents a linear map from vectors to scalars. The dot product operator involving vectors is a good example of
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
travel, tourism, insurance
VECTOR MAP
VECTOR MAP
VECTOR MAP
VECTOR MAP
VECTOR MAP
VECTOR MAP
VECTOR MAP
VECTOR MAP
VECTOR MAP
travel, tourism, insurance