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) ${\displaystyle \cong }$ 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