In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension. Like...
10 KB (1,336 words) - 00:07, 24 January 2024
geometry, a supporting hyperplane of a set S {\displaystyle S} in Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is a hyperplane that has both of the...
6 KB (749 words) - 12:50, 2 March 2023
In geometry, the hyperplane separation theorem is a theorem about disjoint convex sets in n-dimensional Euclidean space. There are several rather similar...
21 KB (2,670 words) - 07:25, 28 September 2023
arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S. Questions about a hyperplane arrangement...
13 KB (1,804 words) - 06:29, 11 January 2024
In geometry, any hyperplane H of a projective space P may be taken as a hyperplane at infinity. Then the set complement P ∖ H is called an affine space...
3 KB (346 words) - 21:28, 14 July 2023
In mathematics, a hyperplane section of a subset X of projective space Pn is the intersection of X with some hyperplane H. In other words, we look at...
2 KB (231 words) - 05:17, 6 April 2023
Tautological bundle (redirect from Hyperplane divisor)
dual of the hyperplane bundle or Serre's twisting sheaf O P n ( 1 ) {\displaystyle {\mathcal {O}}_{\mathbb {P} ^{n}}(1)} . The hyperplane bundle is the...
14 KB (2,441 words) - 11:51, 28 December 2023
specifically in algebraic geometry and algebraic topology, the Lefschetz hyperplane theorem is a precise statement of certain relations between the shape...
12 KB (1,762 words) - 06:17, 8 June 2024
a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2)...
9 KB (1,154 words) - 00:30, 15 March 2024
hyperplane. This is called a linear classifier. There are many hyperplanes that might classify the data. One reasonable choice as the best hyperplane...
64 KB (9,010 words) - 22:17, 18 August 2024