Also see Quaternions and spatial rotation for more information about modeling three-dimensional rotations using quaternions. The values of these three rotations are called Euler angles. Euler angles can be defined by elemental geometry or by composition of rotations. Euler angles can be defined by intrinsic rotations. Matrices of all proper rotations form the special orthogonal group. Therefore, they are valuable in crop rotations. The transformation matrix is proper orthogonal in order to allow rotations but no reflections. This is equivalent to any number of full rotations around any axis. This makes it favorable for integration in many crop rotations. Many algorithms use orthogonal matrices like Householder reflections and Givens rotations for this reason. The Laplacian is invariant under all Euclidean transformations&colon; rotations and translations. Thus, the symmetry group of the sphere with proper rotations is formula 13. The concatenation of all the Givens rotations forms the orthogonal "Q" matrix. Therefore, there are two commuting subgroups of the set of four dimensional rotations. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts.