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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 wikiPageID "4739827".
- Hyperplane_separation_theorem wikiPageRevisionID "601917010".
- Hyperplane_separation_theorem hasPhotoCollection Hyperplane_separation_theorem.
- Hyperplane_separation_theorem subject Category:Theorems_in_convex_geometry.
- Hyperplane_separation_theorem type Abstraction100002137.
- Hyperplane_separation_theorem type Communication100033020.
- Hyperplane_separation_theorem type Message106598915.
- Hyperplane_separation_theorem type Proposition106750804.
- Hyperplane_separation_theorem type Statement106722453.
- Hyperplane_separation_theorem type Theorem106752293.
- Hyperplane_separation_theorem type TheoremsInConvexGeometry.
- 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 m.0cktg4.
- Hyperplane_separation_theorem sameAs Q6795830.
- Hyperplane_separation_theorem sameAs Q6795830.
- Hyperplane_separation_theorem sameAs Hyperplane_separation_theorem.
- Hyperplane_separation_theorem wasDerivedFrom Hyperplane_separation_theorem?oldid=601917010.
- Hyperplane_separation_theorem depiction Separating_axis_theorem2008.png.
- Hyperplane_separation_theorem isPrimaryTopicOf Hyperplane_separation_theorem.
