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Generalization of finite measure to Banach spaces
In mathematics, a vector measure is a function defined on a family of sets and taking vector values satisfying certain properties. It is a generalization
Vector_measure
Similarity measure for number sequences
In data analysis, cosine similarity is a measure of similarity between two non-zero vectors defined in an inner product space. Cosine similarity is the
Cosine_similarity
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)
Subject in mathematics
In mathematics, measure theory in topological vector spaces refers to the extension of measure theory to topological vector spaces. Such spaces are often
Measure theory in topological vector spaces
Measure_theory_in_topological_vector_spaces
Generalized notion of measure in mathematics
representation theorem. Angular displacement Complex measure Spectral measure Vector measure Riesz–Markov–Kakutani representation theorem Signed arc
Signed_measure
Generalization of mass, length, area and volume
measure Product measure Pushforward measure Random measure Regular measure Vector measure Valuation (measure theory) Volume form One way to rephrase our definition
Measure_(mathematics)
Topics referred to by the same term
limit theorem Lyapunov vector-measure theorem, theorem in measure theory that the range of any real-valued, non-atomic vector measure is compact and convex
Lyapunov_theorem
transform of a measure applied to the associated Stieltjes measure, the conventional Laplace transform cannot handle vector measures: measures with values
Laplace–Stieltjes_transform
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
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)
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)
Measure of local oscillation behavior
} is a signed measure: its total variation is defined as above. This definition works also if μ {\displaystyle \mu } is a vector measure: the variation
Total_variation
Mathematical measure of how much a curve or surface deviates from flatness
along the curve. Curvature measures the angular rate of change of the direction of the tangent line, or the unit tangent vector, of the curve per unit distance
Curvature
cylinder set measure (or promeasure, or premeasure, or quasi-measure, or CSM) is a kind of prototype for a measure on an infinite-dimensional vector space.
Cylinder_set_measure
Stochastic way of assigning quantities across a space
(generally vector valued) random variables X n {\displaystyle X_{n}} . The diffuse component μ d {\displaystyle \mu _{d}} is null for a counting measure. In
Random_measure
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
Measure with complex values
complex measures is a Banach space. Riesz representation theorem Signed measure Vector measure Tao, Terence (2011-09-14). An Introduction to Measure Theory
Complex_measure
Instrument used for measuring horizontal velocity in the upper ocean
A vector measuring current meter (VMCM) is an instrument used for obtaining measurements of horizontal velocity in the upper ocean, which exploits two
Vector measuring current meter
Vector_measuring_current_meter
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
Representation learning technique
represented by the embeddings. If the vectors are normalized to have a magnitude of 1, then the similarity measures are proportional to cos ( θ a b )
Embedding_(machine_learning)
Device that measures magnetism
used for those measuring greater than 1 mT. There are two basic types of magnetometer measurement. Vector magnetometers measure the vector components of
Magnetometer
Concept in mathematics
space Bochner measurable function Pettis integral Vector measure – Generalization of finite measure to Banach spaces Weakly measurable function Ardent
Bochner_integral
Property determining comparison and ordering
the measure of units between a number and zero. In vector spaces, the Euclidean norm is a measure of magnitude used to define a distance between two points
Magnitude_(mathematics)
Generalized measurement in quantum mechanics
quantum mechanics Density matrix Quantum operation Projection-valued measure Vector measure Peres, Asher; Terno, Daniel R. (2004). "Quantum information and
POVM
Function spaces generalizing finite-dimensional p norm spaces
functional analysis, and of topological vector spaces. Because of their key role in the mathematical analysis of measure and probability spaces, Lebesgue spaces
Lp_space
Mathematical identities
k are the unit vectors for the x-, y-, and z-axes, respectively. As the name implies the curl is a measure of how much nearby vectors tend in a circular
Vector_calculus_identities
Generalization of the one-dimensional normal distribution to higher dimensions
normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination
Multivariate normal distribution
Multivariate_normal_distribution
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
Set of methods for supervised statistical learning
In machine learning, support vector machines (SVMs, also support vector networks) are supervised max-margin models with associated learning algorithms
Support_vector_machine
Measure of directional electromagnetic energy flux
In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or
Poynting_vector
In mathematics, vector space of linear forms
In mathematics, any vector space V {\displaystyle V} has a corresponding dual vector space (or just dual space for short) consisting of all linear forms
Dual_space
Measure used in functional analysis
ξ {\displaystyle \xi } is a unit vector. Example Let ( X , M , μ ) {\displaystyle (X,M,\mu )} be a σ-finite measure space and, for all E ∈ M {\displaystyle
Projection-valued_measure
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
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
Kind of mathematical function
dynamical system – Subject of study in ergodic theory Vector measure – Generalization of finite measure to Banach spaces Weakly measurable function Strichartz
Measurable_function
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
Property of space that quantifies the magnetic influence at a given location
the cross product. In other words, [T]he command, "Measure the direction and magnitude of the vector B at such and such a place," calls for the following
Magnetic_field
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
integral to vector-valued functions on a measure space, by exploiting duality. The integral was introduced by Gelfand for the case when the measure space is
Pettis_integral
Class of routing protocols
distance-vector routing protocol in data networks determines the best route for data packets based on distance. Distance-vector routing protocols measure the
Distance-vector routing protocol
Distance-vector_routing_protocol
Result about when a matrix can be diagonalized
diagonalization is relatively straightforward for operators on finite-dimensional vector spaces but requires some modification for operators on infinite-dimensional
Spectral_theorem
Real-valued function that quantifies similarity between two objects
similarity measure for real-valued vectors, used in (among other fields) information retrieval to score the similarity of documents in the vector space model
Similarity_measure
Vector field that is the gradient of some function
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
Conservative_vector_field
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
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
Class of Banach spaces
used to define the integral with respect to vector measures, and especially vector-valued Radon measures. The topological duality ba(Σ) = B(Σ)* is easy
Ba_space
Type of mathematical measure
In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff
Radon_measure
Property of certain normed spaces
{\displaystyle E} ) lacks this property. The image of a strictly additive vector measure has the Banach-Saks property. If a Banach space E {\displaystyle E}
Banach-Saks_property
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
Sums of sets of vectors are nearly convex
sets in a vector space. The lemma may be intuitively understood as saying that, if the number of summed sets exceeds the dimension of the vector space, then
Shapley–Folkman_lemma
Euclidean space without distance and angles
point, the zero vector is called the origin. Adding a fixed vector to the elements of a linear subspace (vector subspace) of a vector space produces an
Affine_space
Model for representing text documents
Vector space model (VSM) or term vector model is an algebraic model for representing text documents (or more generally, items) as vectors such that the
Vector_space_model
Separation between two points
or a magnitude, displacement is a vector quantity with both magnitude and direction. In general, the vector measuring the difference between two locations
Distance
Type of topological space
in mathematics Vector measure – Generalization of finite measure to Banach spaces Vector-valued functions – Function valued in a vector space; typically
Bochner_space
Space of bounded sequences
mathematics, ℓ ∞ {\displaystyle \ell ^{\infty }} , the (real or complex) vector space of bounded sequences with the supremum norm, and L ∞ = L ∞ ( X , Σ
L-infinity
Type of personality test
Activity vector analysis (AVA) is a psychometric questionnaire designed to measure four personality factors or vectors: aggressiveness, sociability, emotional
Activity_vector_analysis
Method in natural language processing
application to measure similarity between words, phrases, or entire documents. The first generation of semantic space models is the vector space model for
Word_embedding
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
Class of algorithms for pattern analysis
algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These methods involve using linear classifiers to solve nonlinear
Kernel_method
Mathematical representation of absence of a value
vector). In a vector space, the null vector is the neutral element of vector addition; depending on the context, a null vector may also be a vector mapped
Null_(mathematics)
A vector signal analyzer is an instrument that measures the magnitude and phase of the input signal at a single frequency within the IF bandwidth of the
Vector_signal_analyzer
Vector operator in vector calculus
divergence of a vector field is the extent to which the vector field flux behaves like a source or a sink at a given point. It is a local measure of its "outgoingness"
Divergence
Vector field on a pseudo-Riemannian manifold that preserves the metric tensor
mathematics and theoretical physics, a Killing vector field or Killing field (named after Wilhelm Killing) is a vector field on a Riemannian manifold or pseudo-Riemannian
Killing_vector_field
Binary feedback controller
Press. pp. viii+136. MR 0420366. Kluvánek, Igor; Knowles, Greg (1976). Vector measures and control systems. North-Holland Mathematics Studies. Vol. 20. New
Bang–bang_control
Area of mathematics
branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner
Functional_analysis
Performance measure of a digital radio
The error vector magnitude or EVM (sometimes also called relative constellation error or RCE) is a measure used to quantify the performance of a digital
Error_vector_magnitude
Instrument that measures the network parameters of electrical networks
analyzers are scalar network analyzer (SNA)—measures amplitude properties only vector network analyzer (VNA)—measures both amplitude and phase properties A
Network_analyzer_(electrical)
Dimension of the column space of a matrix
in turn, is identical to the dimension of the vector space spanned by its rows. Rank is thus a measure of the "nondegenerateness" of the system of linear
Rank_(linear_algebra)
space Pettis integral Vector measure – Generalization of finite measure to Banach spaces Pettis, B. J. (1938). "On integration in vector spaces". Trans. Amer
Weakly_measurable_function
Mathematical function that outputs real values
) {\displaystyle {\mathcal {F}}(X,{\mathbb {R} })} may be turned into a vector space and a commutative algebra over the reals with the following operations:
Real-valued_function
Study of discrete mathematical structures
distribution, difference equations, discrete dynamical systems, and discrete vector measures. In discrete calculus and the calculus of finite differences, a function
Discrete_mathematics
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)
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
Measurement on a normed vector space
dual norm is a measure of size for a continuous linear function defined on a normed vector space. Let X {\displaystyle X} be a normed vector space with norm
Dual_norm
Line or vector perpendicular to a curve or a surface
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve
Normal_(geometry)
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
Statistical measure
deviation (RMSD) or root mean square error (RMSE) is a frequently used measure of the distances between actual observed values and an estimation of them
Root_mean_square_deviation
Property of functions
n . {\displaystyle n.} Ma, Tsoy-Wo (2002). Banach–Hilbert spaces, vector measures, group representations. World Scientific. p. 620pp. ISBN 981-238-038-8
Uniform_boundedness
Left-invariant (or right-invariant) measure on locally compact topological group
In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral
Haar_measure
"Pushed forward" from one measurable space to another
to normalization, the Haar measure for the compact, connected Lie group Tn. Gaussian measures on infinite-dimensional vector spaces are defined using the
Pushforward_measure
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
Multivariate derivative (mathematics)
In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued
Gradient
Israeli mathematician (born 1949)
Hebrew University. His MSc thesis was on the subject of “The Range of a Vector Measure” and was supervised by Joram Lindenstrauss. His PhD thesis, "Values
Abraham_Neyman
Number of bits that differ between two strings
strings or vectors of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum
Hamming_distance
Type of vector space in math
spaces of any finite or infinite dimension. A Hilbert space is an abstract vector space, and it has the additional structure of an inner product that allows
Hilbert_space
Two channel voltmeter that also measures phase
A vector voltmeter is a two-channel high-frequency sampling voltmeter that measures phase as well as voltage of two input signals of the same frequency
Vector_voltmeter
Mathematical folklore
Lebesgue measure is a measure defined on infinite-dimensional normed vector spaces, such as Banach spaces, which resembles the Lebesgue measure used in
Infinite-dimensional Lebesgue measure
Infinite-dimensional_Lebesgue_measure
space – Basic object in measure theory; set and a sigma-algebra Pettis integral Vector measure – Generalization of finite measure to Banach spaces Weakly
Bochner_measurable_function
Measure of similarity and diversity between sets
equivalent information (symmetry), the SMC is a better measure of similarity. For example, vectors of demographic variables stored in dummy variables, such
Jaccard_index
Random variable with multiple component dimensions
is the probability measure (a function returning each event's probability). Every random vector gives rise to a probability measure on R n {\displaystyle
Multivariate_random_variable
Function from sets to numbers
the codomain is instead some vector space, as with vector measures, complex measures, and projection-valued measures. The domain of a set function may
Set_function
Turning force around an axis
torque vector is perpendicular to both the position and force vectors, and defines the plane in which the two vectors lie. The resulting torque vector direction
Torque
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
Mathematical concept
187–188. ISBN 978-0-387-94549-1. Diestel, J. and Uhl, J. (1977). Vector measures, Mathematical Surveys 15, American Mathematical Society, Providence
Uniform_integrability
Expressing a measure as an integral of another
Analysis II: Real analysis. Addison-Wesley. Contains a proof for vector measures assuming values in a Banach space. Royden, H. L.; Fitzpatrick, P. M
Radon–Nikodym_theorem
Duality for locally compact abelian groups
analogous to the dual vector space of a vector space: a finite-dimensional vector space V {\displaystyle V} and its dual vector space V ∗ {\displaystyle
Pontryagin_duality
learning vector quantization (LVQ) is a prototype-based supervised classification algorithm. LVQ is the supervised counterpart of vector quantization
Learning_vector_quantization
Expression that may be integrated over a region
tangent vector at all. Since a vector field on N determines, by definition, a unique tangent vector at every point of N, the pushforward of a vector field
Differential_form
Indicator for how well data points fit a line or curve
a vector y=[y1, ..., yn]T), each associated with a fitted (or modeled, or predicted) value f1, ..., fn (known as fi, or sometimes ŷi, as a vector f)
Coefficient_of_determination
Generalization of finite-dimensional Euclidean spaces different from Hilbert spaces
In mathematics, nuclear spaces are topological vector spaces that can be viewed as a generalization of finite-dimensional Euclidean spaces and share many
Nuclear_space
VECTOR MEASURE
VECTOR MEASURE
Boy/Male
Christian & English(British/American/Australian)
Steadfast
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
Boy/Male
Australian, Basque, Czech, Czechoslovakian, Danish, Finnish, French, German, Hungarian, Latin, Polish, Slovenia, Swedish, Swiss, Ukrainian
The Conqueror; Victory; Victorious; Conquer
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.
Male
Arthurian
, sir Hector de Maris; (defender).
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
Boy/Male
English American
Doctor; teacher.
Male
Scandinavian
 Scandinavian form of Roman Latin Victor, VIKTOR means "conqueror." Compare with another form of Viktor.
Boy/Male
Spanish American Shakespearean Greek Latin
Tenacious.
Boy/Male
Christian & English(British/American/Australian)
Conqueror
Boy/Male
Latin American Spanish
Conqueror.
Male
Portuguese
Portuguese form of Latin Hector, HEITOR means "defend; hold fast."
Boy/Male
Spanish
Victor.
Male
English
Short form of English Sylvester, VESTER means "from the forest."
Male
Portuguese
Galician-Portuguese form of Roman Latin Victor, VITOR means "conqueror."
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
Male
Greek
(á¼ÎºÏ„ωÏ) Variant spelling of Greek Hektor, EKTOR means "defend; hold fast."
Boy/Male
Arthurian Legend
Father of Arthur.
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.
VECTOR MEASURE
VECTOR MEASURE
Boy/Male
Muslim
Protractor, One who worships God
Boy/Male
Greek Latin Biblical
God of wine.
Boy/Male
Spanish English German
Divine helmet.
Boy/Male
Hindu
Gift
Boy/Male
Indian, Malayalam, Traditional
Success
Girl/Female
American, British, English, German, Welsh
Prosperous; Happy; Hardworking; Work; Labour; Bountiful
Boy/Male
Hindu, Indian
Sun Power in
Girl/Female
Indian
Name of a Raga
Boy/Male
Indian, Telugu
Lord Krishna; Lord Venkateswara
Boy/Male
Hindu, Indian, Tamil
Big Brother
VECTOR MEASURE
VECTOR MEASURE
VECTOR MEASURE
VECTOR MEASURE
VECTOR MEASURE
n.
An African weaver bird (Textor alector).
a.
Pertaining to a rector or a rectory; rectoral.
v. t.
To tamper with and arrange for one's own purposes; to falsify; to adulterate; as, to doctor election returns; to doctor whisky.
v. t.
To confer a doctorate upon; to make a doctor.
n.
The turning factor of a quaternion.
n.
A directed quantity, as a straight line, a force, or a velocity. Vectors are said to be equal when their directions are the same their magnitudes equal. Cf. Scalar.
n.
The province of a rector; a parish church, parsonage, or spiritual living, with all its rights, tithes, and glebes.
n.
A term made up of the two parts / + /1 /-1, where / and /1 are vectors.
n.
A pregnant woman; a mother; as, A has a son B by one venter, and a daughter C by another venter; children by different venters.
n.
A mathematical instrument, consisting of two rulers connected at one end by a joint, each arm marked with several scales, as of equal parts, chords, sines, tangents, etc., one scale of each kind on each arm, and all on lines radiating from the common center of motion. The sector is used for plotting, etc., to any scale.
n.
An astronomical instrument, the limb of which embraces a small portion only of a circle, used for measuring differences of declination too great for the compass of a micrometer. When it is used for measuring zenith distances of stars, it is called a zenith sector.
n.
Any mechanical contrivance intended to remedy a difficulty or serve some purpose in an exigency; as, the doctor of a calico-printing machine, which is a knife to remove superfluous coloring matter; the doctor, or auxiliary engine, called also donkey engine.
n.
A belly, or protuberant part; a broad surface; as, the venter of a muscle; the venter, or anterior surface, of the scapula.
n.
The chief elective officer of some universities, as in France and Scotland; sometimes, the head of a college; as, the Rector of Exeter College, or of Lincoln College, at Oxford.
a.
Of or pertaining to victory, or a victor' being a victor; bringing or causing a victory; conquering; winning; triumphant; as, a victorious general; victorious troops; a victorious day.
n.
A contrivance for removing superfluous ink or coloring matter from a roller. See Doctor, 4.
n.
Same as Radius vector.
v. t.
To treat as a physician does; to apply remedies to; to repair; as, to doctor a sick man or a broken cart.
n.
The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.
n.
A woman who wins a victory; a female victor.