SO(5)
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In mathematics, SO(5), also denoted SO5(R) or SO(5,R), is the special orthogonal group of degree 5 over the field R of real numbers, i.e. (isomorphic to) the group of orthogonal 5×5 matrices of determinant 1.
Geometric interpretation[]
SO(5) is a subgroup of the direct Euclidean group E+(5), the group of direct isometries, i.e., isometries preserving orientation, of R5, consisting of elements which leave the origin fixed.
More precisely, we have:
- SO(5) E+(5) / T
where T is the translational group of R5.
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
Categories:
- Lie groups
- Geometry stubs