SO(5)
In mathematics, SO, also denoted SO5 or SO, is the special orthogonal group of degree 5 over the field R of real numbers, i.e. the group of orthogonal 5×5 matrices of determinant 1.
Geometric interpretation
SO 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:
where T is the translational group of R5.