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- Hyperplane_separation_theorem abstract "In geometry, the hyperplane separation theorem is either of two theorems about disjoint convex sets in n-dimensional Euclidean space. In the first version of the theorem, if both these sets are closed and at least one of them is compact, then there is a hyperplane in between them and even two parallel hyperplanes in between them separated by a gap. In the second version, if both disjoint convex sets are open, then there is a hyperplane in between them, but not necessarily any gap. An axis which is orthogonal to a separating hyperplane is a separating axis, because the orthogonal projections of the convex bodies onto the axis are disjoint.The hyperplane separation theorem is due to Hermann Minkowski. The Hahn–Banach separation theorem generalizes the result to topological vector spaces.A related result is the supporting hyperplane theorem. In geometry, a maximum-margin hyperplane is a hyperplane which separates two 'clouds' of points and is at equal distance from the two. The margin between the hyperplane and the clouds is maximal. See the article on Support Vector Machines for more details.".
- Hyperplane_separation_theorem thumbnail Separating_axis_theorem2008.png?width=300.
- Hyperplane_separation_theorem wikiPageExternalLink tutorialA.html.
- Hyperplane_separation_theorem wikiPageExternalLink bv_cvxbook.pdf.
- Hyperplane_separation_theorem wikiPageID "4739827".
- Hyperplane_separation_theorem wikiPageLength "10873".
- Hyperplane_separation_theorem wikiPageOutDegree "21".
- Hyperplane_separation_theorem wikiPageRevisionID "687135443".
- Hyperplane_separation_theorem wikiPageWikiLink Affine_space.
- Hyperplane_separation_theorem wikiPageWikiLink Category:Theorems_in_convex_geometry.
- Hyperplane_separation_theorem wikiPageWikiLink Cauchy_sequence.
- Hyperplane_separation_theorem wikiPageWikiLink Collision_detection.
- Hyperplane_separation_theorem wikiPageWikiLink Convex_set.
- Hyperplane_separation_theorem wikiPageWikiLink Dual_cone_and_polar_cone.
- Hyperplane_separation_theorem wikiPageWikiLink Euclidean_space.
- Hyperplane_separation_theorem wikiPageWikiLink Face_(geometry).
- Hyperplane_separation_theorem wikiPageWikiLink Farkas_lemma.
- Hyperplane_separation_theorem wikiPageWikiLink Geometry.
- Hyperplane_separation_theorem wikiPageWikiLink Hahn–Banach_theorem.
- Hyperplane_separation_theorem wikiPageWikiLink Hermann_Minkowski.
- Hyperplane_separation_theorem wikiPageWikiLink Hyperplane.
- Hyperplane_separation_theorem wikiPageWikiLink Minkowski_addition.
- Hyperplane_separation_theorem wikiPageWikiLink Normal_(geometry).
- Hyperplane_separation_theorem wikiPageWikiLink Support_vector_machine.
- Hyperplane_separation_theorem wikiPageWikiLink Supporting_hyperplane.
- Hyperplane_separation_theorem wikiPageWikiLink Topological_vector_space.
- Hyperplane_separation_theorem wikiPageWikiLink File:Separating_axis_theorem2.svg.
- Hyperplane_separation_theorem wikiPageWikiLink File:Separating_axis_theorem2008.png.
- Hyperplane_separation_theorem wikiPageWikiLinkText "Hyperplane separation theorem".
- Hyperplane_separation_theorem wikiPageWikiLinkText "hyperplane separation theorem".
- Hyperplane_separation_theorem wikiPageWikiLinkText "hyperplane".
- Hyperplane_separation_theorem wikiPageWikiLinkText "maximum margin".
- Hyperplane_separation_theorem wikiPageWikiLinkText "separating hyperplanes".
- Hyperplane_separation_theorem wikiPageUsesTemplate Template:Cite_book.
- Hyperplane_separation_theorem wikiPageUsesTemplate Template:Functional_Analysis.
- Hyperplane_separation_theorem wikiPageUsesTemplate Template:Math_theorem.
- Hyperplane_separation_theorem wikiPageUsesTemplate Template:Reflist.
- Hyperplane_separation_theorem subject Category:Theorems_in_convex_geometry.
- Hyperplane_separation_theorem type Redirect.
- Hyperplane_separation_theorem type Theorem.
- Hyperplane_separation_theorem comment "In geometry, the hyperplane separation theorem is either of two theorems about disjoint convex sets in n-dimensional Euclidean space. In the first version of the theorem, if both these sets are closed and at least one of them is compact, then there is a hyperplane in between them and even two parallel hyperplanes in between them separated by a gap. In the second version, if both disjoint convex sets are open, then there is a hyperplane in between them, but not necessarily any gap.".
- Hyperplane_separation_theorem label "Hyperplane separation theorem".
- Hyperplane_separation_theorem sameAs Q6795830.
- Hyperplane_separation_theorem sameAs Trennungssatz.
- Hyperplane_separation_theorem sameAs 分離超平面定理.
- Hyperplane_separation_theorem sameAs m.0cktg4.
- Hyperplane_separation_theorem sameAs Теорема_про_розділяючу_гіперплощину.
- Hyperplane_separation_theorem sameAs Q6795830.
- Hyperplane_separation_theorem wasDerivedFrom Hyperplane_separation_theorem?oldid=687135443.
- Hyperplane_separation_theorem depiction Separating_axis_theorem2008.png.
- Hyperplane_separation_theorem isPrimaryTopicOf Hyperplane_separation_theorem.