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Orthogonal group

In mathematics, the orthogonal group in dimension n, denoted O(n), is the group of distance-preserving transformations of a Euclidean space of dimension n that preserve a fixed point (the origin), where the group operation is given by composing transformations. The orthogonal group is sometimes called the general orthogonal group, by analogy with the…

Products, In Euclidean geometry & Topology

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Overview

Name

In Euclidean geometry

Group structure

Topology

Of indefinite quadratic form over the reals

Of complex quadratic forms

Over finite fields

The spinor norm

Galois cohomology and orthogonal groups

Lie algebra

Related groups

Principal homogeneous space: Stiefel manifold

Specific transforms

Specific groups

Representation theory

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Orthogonal group

Nodes236
Edges235
Triples121
Avg. degree1.99
Density0.008475
Components1

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Orthogonal group

Top relations

related to External links · 11
Orthogonal group → Baez, EMS Press, Encyclopedia, Italian, John Baez, Mathematical Physics, Mathematics, Octonions, Orthogonal, Special Orthogonal Group, This Week's Finds
related to Lie algebra · 11
Orthogonal group → Bk, Dr, It, Lie, One Lie, Over, Since, SO, Spin, The, The Lie
related to Low-dimensional topology · 9
Orthogonal group → RP3, S0, S1, S3, SO, Spin, SU, Symmetry, The
related to Galois cohomology and orthogonal groups · 8
Orthogonal group → As, Clifford, Galois, Galois H1, In, The, They, This
related to Orthogonal groups of characteristic 2 · 8
Orthogonal group → Any, Compare, Formerly, Householder, In, Over, The, Witt
related to Dickson invariant · 6
Orthogonal group → Algebraically, Dickson, For, Over, Taylor, Theorem
related to Of complex quadratic forms · 6
Orthogonal group → As, It, Over, SO, The, Thus
related to Principal homogeneous space: Stiefel manifold · 6
Orthogonal group → Concretely, In, Rn, Stiefel, The, Vn
related to As algebraic groups · 5
Orthogonal group → ATA, Moreover, Since, The, This
related to Discrete subgroups · 5
Orthogonal group → As, Coxeter, Dimension, In, These

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Important terminology

group orthogonal two dimension groups form determinant matrices displaystyle characteristic space one matrix quadratic field spin vector lie subgroup product

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Orthogonal groupis aalgebraic group and a Lie group0.90text
Orthogonal groupis ainternal semidirect product of SO0.90text
Orthogonal groupis akernel of the Dickson invariant and usually has index 2 in O0.90text
Orthogonal groupis asubgroup of the symplectic group0.90text
Orthogonal grouprelated to As algebraic groupsThe0.60section
Orthogonal grouprelated to As algebraic groupsATA0.60section
Orthogonal grouprelated to As algebraic groupsSince0.60section
Orthogonal grouprelated to As algebraic groupsThis0.60section
Orthogonal grouprelated to As algebraic groupsMoreover0.60section
Orthogonal grouprelated to Characteristic different from twoOver0.60section
Orthogonal grouprelated to Characteristic different from twoTwo0.60section
Orthogonal grouprelated to Characteristic different from twoThe0.60section

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