Rotation in the Space

The position of a point after some rotation about the origin can simply be obtained by multiplying its coordinates with a matrix. One reason for introducing homogeneous coordinates is to be able to describe translation by a matrix so that multiple transformations, whether each is a rotation or a translation, can be concatenated into one described by the product of their respective matrices. However, in some applications (such as spaceship tracking), we need only be concerned with rotations of an object, or at least independently from other transformations. In such a situation, we often need to extract the rotation axis and angle from a matrix which represents the concatenation of multiple rotations. The homogeneous transformation matrix, however, is not well suited for the purpose.