## 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

... and is a point on the boundary of then there exists a 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

... 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

... 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

... Projective

**Hyperplane**s - Projective**Hyperplane**s... 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

... 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 ...