projection-valued measure (or spectral measure) is a function defined on certain subsets of a fixed set and whose values are self-adjoint projections...

by the associated projection operator, and the collection of all the subspaces is then represented by a projection-valued measure. One formulation of...

operator-valued measure (POVM) is a measure whose values are positive semi-definite operators on a Hilbert space. POVMs are a generalization of projection-valued...

Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in...

defined, either as a projection-valued measure Ω T {\displaystyle \Omega _{T}} , or as a one-parameter family of projection-valued measures { Σ λ } {\displaystyle...

theorem proves the existence of a certain projection-valued measure (PVM) Q {\displaystyle Q} , the spectral measure of A {\displaystyle A} . In this case:...

adjoint, E is said to be a projection-valued measure or PVM.) The theorem reads as follows: Let E be a positive L(H)-valued measure on X. There exists a Hilbert...

called the projection postulate. A more general formulation replaces the projection-valued measure with a positive-operator valued measure (POVM). To...

discrete, the projection valued measure reduces to a family {Eλ} indexed on some parameter λ ranging over a countable set. Similarly, a Y valued observable...

{\displaystyle A=\int a\,dP(a)} with a projection-valued measure P {\displaystyle P} . For the expectation value of A {\displaystyle A} in a pure state...

formulation of direct sum decomposition is formulated in terms of projection-valued measures. Mackey's original formulation was expressed in terms of a locally...

The Mercator projection (/mərˈkeɪtər/) is a conformal cylindrical map projection first presented by Flemish geographer and mapmaker Gerardus Mercator...

measurements. That theory was based in turn on the theory of projection-valued measures for self-adjoint operators that had been recently developed (by...

Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in...

a Hilbert space H. A has a spectral decomposition, which is a projection-valued measure E defined on the Borel subsets of R. In particular, for any bounded...

legend from Proctor Valley, east of San Diego, California Projection-valued measure, a type of measure used in functional analysis Perfetti Van Melle, an Italian-Dutch...

This is a summary of map projections that have articles of their own on Wikipedia or that are otherwise notable. Because there is no limit to the number...

In linear algebra and functional analysis, a projection is a linear transformation P {\displaystyle P} from a vector space to itself (an endomorphism)...

A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These...

Riesz-Markov Theorem, τ {\displaystyle \tau } gives rise to a projection-valued measure on R {\displaystyle \mathbb {R} } that is the resolution of the...

the normal operator N gives rise to a projection-valued measure P on its spectrum, σ(N), which assigns a projection PΩ to each Borel subset of σ(N). N can...

for "equal measure", reflecting that the scale along each axis of the projection is the same (unlike some other forms of graphical projection). An isometric...

Throughout, H {\displaystyle H} is a fixed Hilbert space. A projection-valued measure on a measurable space ( X , Ω ) , {\displaystyle (X,\Omega ),}...

or equal-area projection is a map projection that preserves relative area measure between any and all map regions. Equivalent projections are widely used...

terms of self-adjoint projections on a separable complex Hilbert space H, that is, in terms of a PVM (Projection-valued measure). In the general case...

countable chains. A POVM is a projection-valued measure precisely when its image is contained in the orthoalgebra of projections on the Hilbert space H {\displaystyle...

of Borel measure Structure theorem for Gaussian measures – Mathematical theorem Projection-valued measure – Mathematical operator-value measure of interest...

gross value added (GVA) is the measure of the value of goods and services produced in an area, industry or sector of an economy. "Gross value added is...

stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane...

Human population projections are attempts to extrapolate how human populations will change in the future. These projections are an important input to forecasts...