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

function for which the space is a complete metric space. A Hilbert space is a special case of a Banach space. Hilbert spaces were studied beginning in the first...

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)...

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

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...

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

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

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

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

\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...

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...

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

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

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

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

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

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

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, 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...

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...

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

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...

hypercube or a set of scattered points. The diameter or metric diameter of a subset of a metric space is the least upper bound of the set of all distances...

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...

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...

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 → [...

of f itself. Liouville's equation was also taken as an example by David Hilbert in the formulation of his nineteenth problem. By using the change of variables...

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

In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces. Thus it is a separable Hausdorff space in which each point has a neighbourhood...

scalar curvature Kähler metrics (cscK metrics). In 1954, Eugenio Calabi formulated a conjecture about the existence of Kähler metrics on compact Kähler manifolds...