Simple, Double and Isoclinic Rotations with a Viable Algorithm

The main topic of this study is to investigate rotation matrices in four dimensional Euclidean space in twodifferent ways. The first of these ways is Rodrigues formula and the second is Cayley formula.The mostimportant common point of both formulas is the use of skew symmetric matrices. However, depending onthe skew symmetric matrix used, it is possible to classify the rotation matrices by both formulas. Therefore,it is also revealed how the rotation matrices obtained by both formulas are classified as simple, doubleor isoclinic rotation. Eigenvalues of skew symmetric matrices play the major role in this classification.With the use of all results, it is also seen which skew symmetric matrix is obtained from a given rotationmatrix by Rodrigues and Cayley formula, respectively. Finally, an algorithm for classification of rotationsis given with the help of the obtained data and explained with an example.

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