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bn:00980521n
Noun Concept
Categories: Quadratic forms, Euclidean symmetries, All articles with unsourced statements, Linear algebraic groups, Lie groups
EN
orthogonal group  SO  Complex orthogonal group  Dickson map  general orthogonal group
EN
In mathematics, the orthogonal group in dimension n {\displaystyle n}, denoted O ⁡ {\displaystyle \operatorname {O} }, is the group of distance-preserving transformations of a Euclidean space of dimension n {\displaystyle n} that preserve a fixed point, where the group operation is given by composing transformations. Wikipedia
Definitions
Relations
Sources
EN
In mathematics, the orthogonal group in dimension n {\displaystyle n}, denoted O ⁡ {\displaystyle \operatorname {O} }, is the group of distance-preserving transformations of a Euclidean space of dimension n {\displaystyle n} that preserve a fixed point, where the group operation is given by composing transformations. Wikipedia
Mathematical group consisting of transformations of a Euclidean space which preserve distance and a fixed point Wikidata
For given n and field F (especially where F is the real numbers), the group of n × n orthogonal matrices with elements in F, where the group operation is matrix multiplication. Wiktionary
IS A
simple Lie group
compact space
HAS KIND
hyperoctahedral group
indefinite orthogonal group
SO
HAS INSTANCE
Z2
STUDIED BY
category theory
Wikipedia
EN
orthogonal group
Wikidata
EN
orthogonal group
Wiktionary
EN
orthogonal group
Wikipedia Redirections
EN
Complex orthogonal group, Dickson map, general orthogonal group, Group O(3), Invariant theory of the orthogonal group, O(2), O(3) group, orthogonal groups, orthogonal Lie algebra, rotation group, SO(32), special orthogonal group, special orthogonal Lie algebra, spinor norm
Wikidata Alias
EN
general orthogonal group, O(n)

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