  Elliptical rotation is the motion of a point on an ellipse through some angle
about a vector. The purpose of this paper is to examine the generation of
elliptical rotations and to interpret the motion of a point on an elipsoid
using elliptic inner product and elliptic vector product. To generate an
elliptical rotation matrix, first we define an elliptical ortogonal matrix and
an elliptical skew symmetric matrix using the associated inner product. Then we
use elliptic versions of the famous Rodrigues, Cayley, and Householder methods
to construct an elliptical rotation matrix. Finally, we define elliptic
quaternions and generate an elliptical rotation matrix using those quaternions.
Each method is proven and is provided with several numerical examples.
