SO(5)

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"("n") $cong$ "E"⁺(5) "/ T"where "T" is the translational group of R⁵.

Lie group

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

ee also

*orthogonal matrix
*orthogonal group
*rotation group
*List of simple Lie groups