Orthogonal rotation groups are Lie Groups. The orthogonal rotation group is the set of Real Orthogonal Matrices.

The orthogonal rotation group is the set of Real Orthogonal Matrices (having independent parameters) with Determinant .

The orthogonal rotation group is the set of Real Orthogonal
Matrices, having independent parameters, with Determinant . is
Homeomorphic with . Its elements can be written using Euler Angles and Rotation
Matrices as

(1) | |||

(2) | |||

(3) | |||

(4) |

**References**

Arfken, G. ``Orthogonal Group, .'' *Mathematical Methods for Physicists, 3rd ed.*
Orlando, FL: Academic Press, p. 252-253, 1985.

Wilson, R. A. ``ATLAS of Finite Group Representation.'' http://for.mat.bham.ac.uk/atlas/html/contents.html#orth.

© 1996-9

1999-05-26