About: Hilbert metric

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In mathematics, the Hilbert metric, also known as the Hilbert projective metric, is an explicitly defined distance function on a bounded convex subset of the n-dimensional Euclidean space Rn. It was introduced by David Hilbert as a generalization of Cayley's formula for the distance in the Cayley–Klein model of hyperbolic geometry, where the convex set is the n-dimensional open unit ball. Hilbert's metric has been applied to Perron–Frobenius theory and to constructing Gromov hyperbolic spaces.

Attributes	Values
rdfs:label	Hilbert-Metrik (de) Hilbert metric (en)
rdfs:comment	In der Geometrie sind Hilbert-Metriken gewisse Metriken auf beschränkten konvexen Teilmengen des euklidischen Raumes, die das Beltrami-Klein-Modell der hyperbolischen Geometrie verallgemeinern. (de) In mathematics, the Hilbert metric, also known as the Hilbert projective metric, is an explicitly defined distance function on a bounded convex subset of the n-dimensional Euclidean space Rn. It was introduced by David Hilbert as a generalization of Cayley's formula for the distance in the Cayley–Klein model of hyperbolic geometry, where the convex set is the n-dimensional open unit ball. Hilbert's metric has been applied to Perron–Frobenius theory and to constructing Gromov hyperbolic spaces. (en)
dcterms:subject	Metric geometry
Wikipage page ID	22154619 (xsd:integer)
Wikipage revision ID	1077865147 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Projectivization David Mount Convex set Mathematics Garrett Birkhoff Convex cone Cross-ratio Orthant Trans. Amer. Math. Soc. Arch. Ration. Mech. Anal. Line (geometry) Logarithm Macbeath regions Simplex Closed set Mathematische Annalen Banach space Euclidean space Amer. Math. Monthly Perron–Frobenius theorem Hyperbolic geometry Metric geometry Triangle Publ. Math. Inst. Hautes Études Sci. Open set Klein model Metric (mathematics) Unit ball Cayley metric Gromov hyperbolic space Mathematics Association of America Integral operators Banach contraction principle
Link from a Wikipage to an external page	https://www.cambridge.org/core/books/geometric-group-theory/on-hiberts-metric-for-simplices/8F073A50F15A66D00C59D45ADD7034FC https://www.jstor.org/stable/pdf/2323940.pdf%7Cpublisher https://www.youtube.com/watch%3Fv=XE5x5rAK8Hk https://ghostarchive.org/varchive/youtube/20211220/XE5x5rAK8Hk https://zenodo.org/record/2067884
sameAs	Hilbert metric Hilbert metric Hilbert metric Hilbert metric Hilbert metric
dbp:wikiPageUsesTemplate	dbt:Cbignore dbt:Citation dbt:Cite_arXiv dbt:Cite_book dbt:Cite_journal dbt:Short_description dbt:Harvs
authorlink	David Hilbert (en)
first	David (en)
last	Hilbert (en)
year	1895 (xsd:integer)
has abstract	In der Geometrie sind Hilbert-Metriken gewisse Metriken auf beschränkten konvexen Teilmengen des euklidischen Raumes, die das Beltrami-Klein-Modell der hyperbolischen Geometrie verallgemeinern. (de) In mathematics, the Hilbert metric, also known as the Hilbert projective metric, is an explicitly defined distance function on a bounded convex subset of the n-dimensional Euclidean space Rn. It was introduced by David Hilbert as a generalization of Cayley's formula for the distance in the Cayley–Klein model of hyperbolic geometry, where the convex set is the n-dimensional open unit ball. Hilbert's metric has been applied to Perron–Frobenius theory and to constructing Gromov hyperbolic spaces. (en)
prov:wasDerivedFrom	wikipedia-en:Hilbert_metric?oldid=1077865147&ns=0
page length (characters) of wiki page	8983 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Hilbert_metric
is Link from a Wikipage to another Wikipage of	Macbeath region David Hilbert Algebraic statistics Cross-ratio Cayley–Klein metric Yakov Feld List of things named after David Hilbert Hilbert geometry Hilbert projective metric
is Wikipage redirect of	Hilbert projective metric
is foaf:primaryTopic of	wikipedia-en:Hilbert_metric

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