Rotations and rotation matrices

In molecular replacement, a model, described as a list of orthogonal coordi nates, is to be moved into a new position and orientation. The orthogonal c oordinate system also has to be related to the crystallographic system, whi ch may not be orthogonal, and crystallographic symmetry must be considered, which applies to coordinates expressed as fractions of the unit cell. Elem entary properties of rotation matrices and their representation as polar or Eulerian angles are discussed.