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...

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...

representation theorem. Angular displacement Complex measure Spectral measure Vector measure Riesz–Markov–Kakutani representation theorem Signed arc...

operations on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is...

Outer measure Product measure Pushforward measure Regular measure Vector measure Valuation (measure theory) Volume form One way to rephrase our definition...

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...

transform of a measure applied to the associated Stieltjes measure, the conventional Laplace transform cannot handle vector measures: measures with values...

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...

In mathematics, measure theory in topological vector spaces refers to the extension of measure theory to topological vector spaces. Such spaces are often...

distance-vector routing protocol in data networks determines the best route for data packets based on distance. Distance-vector routing protocols measure the...

complex measures is a Banach space. Riesz representation theorem Signed measure Vector measure Tao, Terence (2011-09-14). An Introduction to Measure Theory...

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...

(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...

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...

operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces...

used for those measuring greater than 1 mT. There are two basic types of magnetometer measurement. Vector magnetometers measure the vector components of...

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....

A vector measuring current meter (VMCM) is an instrument used for obtaining measurements of horizontal velocity in the upper ocean, which exploits two...

(usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used...

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...

} 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...

In machine learning, support vector machines (SVMs, also support vector networks) are supervised max-margin models with associated learning algorithms...

or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol...

quantum mechanics Density matrix Quantum operation Projection-valued measure Vector measure Peres, Asher; Terno, Daniel R. (2004). "Quantum information and...

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...

In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or...

normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination...

functional analysis, and of topological vector spaces. Because of their key role in the mathematical analysis of measure and probability spaces, Lebesgue spaces...

finite-dimensional p norm spaces - Vector spaces of measurable functions: the L p {\displaystyle L^{p}} spaces Measure-preserving dynamical system – Subject...

similarity measure for real-valued vectors, used in (among other fields) information retrieval to score the similarity of documents in the vector space model...