What is hyperplane?

Hyperplane

A hyperplane is a concept in geometry. It is a generalization of the plane into a different number of dimensions.

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Some articles on hyperplane:

Supporting Hyperplane Theorem
... and is a point on the boundary of then there exists a supporting hyperplane containing If (the dual space of X) such that for all, then defines a supporting hyperplane ... interior such that every point on the boundary has a supporting hyperplane, then is a convex set ... The hyperplane in the theorem may not be unique, as noticed in the second picture on the right ...
Locality-sensitive Hashing - Methods - Random Projection
... The basic idea of this technique is to choose a random hyperplane (defined by a normal unit vector ) at the outset and use the hyperplane to hash input vectors ... Given an input vector and a hyperplane defined by, we let ... That is, depending on which side of the hyperplane lies ...
Point Reflection - Terminology
... More narrowly, a "reflection" refers to a reflection in a hyperplane ( dimensional affine subspace – a point on the line, a line in the plane, a plane in 3-spa ... In dimension 1 these coincide, as a point is a hyperplane in the line ... Reflection in a hyperplane has a single −1 eigenvalue (and multiplicity on the 1 eigenvalue), while point reflection has only the −1 eigenvalue (with multiplicity n) ...
Special Types of Hyperplanes - Projective Hyperplanes
... Projective hyperplanes, are used in projective geometry ... An affine hyperplane together with the associated points at infinity forms a projective hyperplane ... One special case of a projective hyperplane is the infinite or ideal hyperplane, which is defined with the set of all points at infinity ...
Supporting Hyperplane
... Supporting hyperplane is a concept in geometry ... A hyperplane divides a space into two half-spaces ... A hyperplane is said to support a set in Euclidean space if it meets both of the following is entirely contained in one of the two closed half-spaces determined by the ...