Abstract: The position of a point after some rotation about the origin can simply be obtained by multiplyingits coordinates with a matrix. One reason for introducing homogeneous coordinates is tobe able to describe translation with a matrix so that multiple transformations, whether each is arotation or a translation, can be concatenated into one described by the product of their respectivematrices. However, in some applications (such as spaceship tracking), we need only be concernedwith 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 theconcatenation of multiple rotations. The homogeneous transformation matrix, however, is not wellsuited for the purpose.