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- Q6795830 subject Q8851971.
- Q6795830 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.".
- Q6795830 thumbnail Separating_axis_theorem2008.png?width=300.
- Q6795830 wikiPageExternalLink tutorialA.html.
- Q6795830 wikiPageExternalLink bv_cvxbook.pdf.
- Q6795830 wikiPageWikiLink Q1134296.
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- Q6795830 wikiPageWikiLink Q8087.
- Q6795830 wikiPageWikiLink Q866116.
- Q6795830 wikiPageWikiLink Q8851971.
- Q6795830 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.".
- Q6795830 label "Hyperplane separation theorem".
- Q6795830 depiction Separating_axis_theorem2008.png.