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.
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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)where T is the translational group of R5.
Lie group
SO(5) is a simple Lie group of dimension 10.
References
SO(5) Wikipedia(Text) CC BY-SA