In mathematics, the Hilbert metric, also known as the Hilbert projective metric, is an explicitly defined distance function on a bounded convex subset...
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mathematics, a Hilbert space is a real or complex inner product space that is also a complete metric space with respect to the metric induced by the inner...
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metric for which the lines of the projective space are geodesics. Metrics of this type are called flat or projective. Thus, the solution of Hilbert's...
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Stress–energy tensor (redirect from Hilbert stress-energy tensor)
Baker, M.R.; Kiriushcheva, N.; Kuzmin, S. (2021). "Noether and Hilbert (metric) energy–momentum tensors are not, in general, equivalent". Nuclear...
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infinite-dimensional Hilbert metric, a metric that makes a bounded convex subset of a Euclidean space into an unbounded metric space This disambiguation...
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Hilbert cube as a metric space, indeed as a specific subset of a separable Hilbert space (that is, a Hilbert space with a countably infinite Hilbert basis)...
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as the metric induced by the flat space Euclidean metric, after appropriate changes of variable. When extended to complex projective Hilbert space, it...
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Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several...
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David Hilbert Foundations of geometry Hilbert C*-module Hilbert cube Hilbert curve Hilbert matrix Hilbert metric Hilbert–Mumford criterion Hilbert number...
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The Einstein–Hilbert action in general relativity is the action that yields the Einstein field equations through the stationary-action principle. With...
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In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field...
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P_{+}-P_{-}} is called the (real phase) metric operator or fundamental symmetry, and may be used to define the Hilbert inner product ( ⋅ , ⋅ ) {\displaystyle...
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Generalization of metric spaces Generalized metric space Hilbert's fourth problem – Construct all metric spaces where lines resemble those on a sphere Metric tree...
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product of two Hilbert spaces is another Hilbert space. Roughly speaking, the tensor product is the metric space completion of the ordinary tensor product...
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Pseudo-Riemannian manifold (redirect from Pseudo-Riemannian metric)
called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian...
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Polish space (redirect from Polish metric space)
group of a separable Hilbert space (with the strong operator topology) is a Polish group. The group of homeomorphisms of a compact metric space is a Polish...
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Inner angle may refer to: internal angle of a polygon Fubini–Study metric on a Hilbert space This disambiguation page lists mathematics articles associated...
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\mathbf {P} ^{n-1}} , which carries a Kähler metric, called the Fubini–Study metric, derived from the Hilbert space's norm. As such, the projectivization...
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non-Euclidean geometry was given by A'Campo and Papadopoulos (2014). Hilbert metric Cayley (1859), p. 82, §§209–229 Klein (1871) Klein (1873) Klein (1893a)...
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In mathematics, the Kadison–Kastler metric is a metric on the space of C*-algebras on a fixed Hilbert space. It is the Hausdorff distance between the...
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Riemannian manifold (redirect from Riemannian metric)
T_{x}M} . If g {\displaystyle g} is a strong Riemannian metric, then M {\displaystyle M} must be a Hilbert manifold.[citation needed] If ( H , ⟨ ⋅ , ⋅ ⟩ ) {\displaystyle...
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space, the result is a Hilbert space containing the original space as a dense subspace. Completeness is a property of the metric and not of the topology...
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Separable space (redirect from Separable metric space)
is separable. X is metrizable. Every separable metric space is homeomorphic to a subset of the Hilbert cube. This is established in the proof of the Urysohn...
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Metrizable space (category Metric spaces)
homeomorphic to a metric space. That is, a topological space ( X , τ ) {\displaystyle (X,\tau )} is said to be metrizable if there is a metric d : X × X → [...
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The gap metric is a mathematical concept used to quantify the distance between linear operators on a Hilbert space. It was introduced independently by...
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scheduling Hilbert field Hilbert function Hilbert manifold Hilbert matrix Hilbert metric Hilbert modular form Hilbert modular variety Hilbert–Mumford criterion...
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Inner product space (redirect from Pre-Hilbert space)
In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation...
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homeomorphic to some open subset of a given Banach space (metric Hilbert manifolds and metric Fréchet manifolds are defined similarly). For example, every...
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positive genus exists, using the Abel–Jacobi map and theta functions. Hilbert metric A theorem on the anharmonic ratio of lines appeared in the work of Pappus...
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Taxicab geometry (redirect from Taxi metric)
differences of their respective Cartesian coordinates, a distance function (or metric) called the taxicab distance, Manhattan distance, or city block distance...
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