Hyperplane

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Applications

Convex geometry Disjoint Convex sets Hyperplane separation theorem Support vector machines

11 related topics

Special types of hyperplanes

Cartesian coordinates Linear equation Connected components Complement Inequalities

12 related topics

Overview

Geometry Two-dimensional plane Three-dimensional space Mathematical spaces Dimension

39 related topics

Technical description

N-dimensional space Vector space Coordinates Algebraic equation Linear subspaces

7 related topics

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Geometry
Two-dimensional plane Plane (geometry)
Three-dimensional space
Mathematical spaces Space (mathematics)
Dimension
Plane in space Euclidean planes in three-dimensional space
Flat Flat space
Hypersurface
Subspace Subspace (mathematics)
Ambient space
One-dimensional
Lines Line (geometry)
Zero-dimensional
Points Point (geometry)
Euclidean space
"flats" Flat (geometry)
Half spaces Half-space (geometry)
Reflection Reflection (geometry)
Motion Motion (geometry)
Geometric transformation
Distance Distance (mathematics)
Group Group (mathematics)
Generated Generating set of a group
Convex polytope
Intersection Intersection (set theory)
Non-Euclidean geometry
N-dimensional sphere N-sphere
Hyperbolic space
Pseudo-Riemannian Pseudo-Riemannian manifold
Space form

Dihedral angles

Dihedral angle
Normal vectors Normal vector
Rotation Rotation (mathematics)
Subspace Euclidean subspace

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Nodes79

Edges78

Triples37

Avg. degree1.97

Density0.025316

Components1

How this topic connects Entity context

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Hyperplane

Top relations

is a · 8

Hyperplane → affine subspace of codimension 1 in an affine space, flat hypersurface, generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension, infinite or ideal hyperplane, kind of motion, linear subspace of codimension 1, solution of a single linear equation, solution of a single linear equation.Projective hyperplanesProjective hyperplanes are used in projective geometry

related to Projective hyperplanes · 5

Hyperplane → An, In, One, Projective, The

related to External links · 4

Hyperplane → Eric, Flat, MathWorld, Weisstein

related to Technical description · 4

Hyperplane → Euclidean, If, In, The

related to Affine hyperplanes · 3

Hyperplane → An, In, In Cartesian

has application · 2

Hyperplane → Euclidean, In

related to Dihedral angles · 2

Hyperplane → Euclidean, The

related to Special types of hyperplanes · 2

Hyperplane → Several, Some

related to Vector hyperplanes · 2

Hyperplane → In, Such

related to Support hyperplanes · 1

Hyperplane → The

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

space hyperplanes subspace two geometry affine dimension codimension projective ambient points euclidean one plane spaces vector linear n-dimensional concept distance

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Hyperplane	is a	generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension	0.90	text
Hyperplane	is a	flat hypersurface	0.90	text
Hyperplane	is a	kind of motion	0.90	text
Hyperplane	is a	affine subspace of codimension 1 in an affine space	0.90	text
Hyperplane	is a	linear subspace of codimension 1	0.90	text
Hyperplane	is a	solution of a single linear equation.Projective hyperplanesProjective hyperplanes are used in projective geometry	0.90	text
Hyperplane	is a	infinite or ideal hyperplane	0.90	text
Hyperplane	is a	solution of a single linear equation	0.90	text
elliptic space or projective space	instance of	In a non-orientable space	0.80	text
there is no concept of half-planes	instance of	In a non-orientable space	0.80	text
linear-combination	instance of	Affine hyperplanes are used to define decision boundaries in many machine learning algorithms	0.80	text
Hyperplane	has application	In	0.60	section

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Connections between topic areas Semantic bridges

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Min side: 3

Research this topic

Explore this topic

Applications

Special types of hyperplanes

Overview

Technical description

Key facts & relationships

Topics to explore

Overview

Technical description

Special types of hyperplanes

Applications

Dihedral angles

Advanced semantic analysis

Map overview Semantic statistics

Hyperplane

How this topic connects Entity context

Hyperplane

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges