In mathematics, the Hilbert metric, also known as the Hilbert projective metric, is an explicitly defined distance function on a bounded convex subset...

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...

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...

Baker, M.R.; Kiriushcheva, N.; Kuzmin, S. (2021). "Noether and Hilbert (metric) energy–momentum tensors are not, in general, equivalent". Nuclear...

as the metric induced by the flat space Euclidean metric, after appropriate changes of variable. When extended to complex projective Hilbert space, it...

The Einstein–Hilbert action in general relativity is the action that yields the Einstein field equations through the stationary-action principle. With...

David Hilbert Foundations of geometry Hilbert C*-module Hilbert cube Hilbert curve Hilbert matrix Hilbert metric Hilbert–Mumford criterion Hilbert number...

infinite-dimensional Hilbert metric, a metric that makes a bounded convex subset of a Euclidean space into an unbounded metric space This disambiguation...

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...

P_{+}-P_{-}} is called the (real phase) metric operator or fundamental symmetry, and may be used to define the Hilbert inner product ( ⋅ , ⋅ ) {\displaystyle...

Generalization of metric spaces Generalized metric space Hilbert's fourth problem – Construct all metric spaces where lines resemble those on a sphere Metric tree...

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...

product of two Hilbert spaces is another Hilbert space. Roughly speaking, the tensor product is the metric space completion of the ordinary tensor product...

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)...

\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...

In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field...

scheduling Hilbert field Hilbert function Hilbert manifold Hilbert matrix Hilbert metric Hilbert modular form Hilbert modular variety Hilbert–Mumford criterion...

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)...

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...

Inner angle may refer to: internal angle of a polygon Fubini–Study metric on a Hilbert space This disambiguation page lists mathematics articles associated...

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...

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 → [...

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...

on the groups of translations and isometries. On the other hand, David Hilbert proposed a set of axioms, inspired by Euclid's postulates. They belong...

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...

space, named after Jacques Hadamard, is a non-linear generalization of a Hilbert space. In the literature they are also equivalently defined as complete...

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...

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...

called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian...

homeomorphic to some open subset of a given Banach space (metric Hilbert manifolds and metric Fréchet manifolds are defined similarly). For example, every...