Special orthogonal group:SO(3,R)

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VIEW FACTS ABOUT THIS GROUP: All factsGroup property satisfactionsSubgroup property satisfactionsGroup property dissatisfactionsSubgroup property satisfactions
VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

This group, denoted $SO(3,\mathbb{R})$, is the special orthogonal group for the standard dot product over the field of real numbers in three dimensions. Explicitly, it is given by:

$\{A\in GL(3,\mathbb{R})\mid A{A}^T=\text{Identity matrix},detA=1\}$

Arithmetic functions

Function	Value	Similar groups	Explanation
dimension of an algebraic group	3		As $SO(n,\_),n=3:n(n-1)/2=3(3-1)/2=3$
dimension of a real Lie group	3		As $SO(n,\mathbb{R}),n=3:n(n-1)/2=3(3-1)/2=3$

Subgroup structure

Further information: classification of finite subgroups of SO(3,R)