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In [[mathematics]], '''SO(5)''', also denoted '''SO<sub>5</sub>(R)''' or '''SO(5,R)''', is the [[special orthogonal group]] of degree 5 over the field '''R''' of [[real number]]s, i.e. ([[isomorphic]] to) the group of [[orthogonal matrix|orthogonal]] 5&times;5 [[Matrix (mathematics)|matrices]] of [[determinant]] 1.

==Geometric interpretation==

SO(5) is a subgroup of the [[Euclidean group#Direct and indirect isometries|direct Euclidean group ''E''<sup>+</sup>(5)]], the group of ''direct'' [[isometry|isometries]], i.e., isometries preserving [[orientation (mathematics)|orientation]], of '''R'''<sup>5</sup>, consisting of elements which leave the origin fixed.

More precisely, we have:
:''SO''(''5'') <math>\cong</math> ''E''<sup>+</sup>(5) ''/ T''
where ''T'' is the [[translation (geometry)|translational]] group of '''R'''<sup>5</sup>.

==Lie group==

SO(5) is a [[simple Lie group]] of dimension 10.

==See also==

*[[Orthogonal matrix]]
*[[Orthogonal group]]
*[[Rotation group SO(3)]]
*[[List of simple Lie groups]]

[[Category:Lie groups]]


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