Special orthogonal group:SO(3,R): Difference between revisions

Revision as of 16:48, 18 September 2012

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
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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 $S O (3, R)$ , is the special orthogonal group for the standard dot product over the field of real numbers in three dimensions. Explicitly, it is given by:

${A \in G L (3, R) ∣ A A^{T} = Identity matrix, det A = 1}$

Arithmetic functions

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

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 | {{arithmetic function value|dimension of an algebraic group|3}} || ||As <math>SO(n,\_), n = 3: n(n - 1)/2 = 3(3 - 1)/2 = 3</math>
 |-
-| {{arithmetic function value|dimension of a real Lie group|3}} || As <math>SO(n,\R), n = 3: n(n - 1)/2 = 3(3 - 1)/2 = 3</math>
+| {{arithmetic function value|dimension of a real Lie group|3}} || || As <math>SO(n,\R), n = 3: n(n - 1)/2 = 3(3 - 1)/2 = 3</math>
 |}