# 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) ${\displaystyle \cong }$ E+(5) / T

where T is the translational group of R5.

## Lie group

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